This is super tiny nitpick, but there's a number-mismatch in the tag-text:

The text should either read

Watch a tag to curate your list of questions and receive optional notifications on that tag's activity.

or

Watch tags to curate your list of questions and receive optional notifications on those tags' activity.

or some third construction I'm not smart enough to notice.

Given the mismatch between the box's heading ("Watched Tags...") and the button's text ("Watch a tag") it's not clear which of the two options above would be better. (And perhaps that's a signal that the heading and the button-text also need agreement.)

Absent a strong feeling on whether we're really trying to talk about tags singly or as a group, I'd suggest the first construction: it's slightly simpler English. (Since it avoids the plural possessive tags'.)

Please make the watched/hidden tag thing hidable/toggle-able, especially on the per-site metas.

The new display takes up a bit more screen real-estate if you have watched tags, or a lot more when you don't, and draws more attention with its glow effect and large image when empty. _{Why is it glowing, btw? It's static and doesn't need to draw attention, and nothing else is glowing}

On the per-site metas, I imagine very few people want to watch/hide specific tags, so it'll likely be empty, and making it pop out like that is distracting and provides very little utility.

Alternatively, you could consider removing the feature altogether on the per-site meta.

Please de-emphasize the Unwatch button

The unwatch button in really inviting and asks to be pressed as 'main' action in the tag-section. This is OK if you accidentally added the tag, but for a normal workflow this is not what a user wants to do.

See this image:

Maybe just a grey button with blueish text is ok?

status-completed

In the new design the two sections having the title as Watched Tags and Ignored tags.
In these for the Ignored tags, the tags can be replaced to Tags for uniformity.

Also I can see Ignored Tags only in the Tag Watching & Ignoring page too.

In this system, what options do I have for dealing with tag conflicts, that is, with questions that have both an ignored tag and a watched tag?

Here's what I see on MSE right now:

Apparently, the "ignored" tags have a higher weight than the "watched" tags – in my example, the ignored behavior causes the second line to gray out even though featured is watched.

Can I have the option to specify that a particular "watched" tag should override any "ignored" tags on the same question, and prevent it from being grayed out or hidden?

The new sidebar widget stands out (in a bad way) because it does not match the style of the existing widgets. Why not keep the style similar?

bug status-completed

If I'm trying to add a synonym tag to the Watched Tags or Ignored tags section in the Question page's side bar, it throws the error as

{tagname} does not exist on this site

For an example, in SO I'm trying with mssql as on of the synonym of sql-server tag.

GIF for reference:

But if I'm trying the same in the Tag Watching & Ignoring under the Edit Profile & Settings, it doesn't throw any error.

GIF for reference:

The validation in the question's page can be applied in the Edit profile & settings page too?

I really like this update. The tag description is easier to read and interact with, the layout is lighter, and makes Watched Tags more understandable in general.

The only suggestion/doubt I got is regarding the "hot" tags being colored, while the others remain with black text. Specifically, the way that coloring is determined:

We can see that both java and vm have the same color tone, even though Java tag has almost 1000x watchers and 200x questions asked. On the other hand, the ruby-on-rails-3.2.1 tag is not colored, but it has almost the same watches as VM, and even more questions asked.

In my mind, I would have expected the color to change (more intense or red) proportionally to the number of watchers and questions asked, similar to the way the vote counter on comment gets more orange/red as the counter increases.

IMHO, this gives a better sense of the "hotness" of the tag, and can perhaps give a "wrong" impression of hotness (i.e.: VM being equally hot to Java when clearly it isn't, and Ruby not being hot when it got almost the same watchers and more questions).

After the change in the name and addition of the icon, we can also watch over things. Are anyone from the designing team following the show? ;)

Jokes apart, I like improvement in popup and removing extra options from it. However, there are some concerns from me.

Boxes take more space in the page

I think the dialogue boxes for watched and ignored tags are occupying more space on the page.

I think this can be reduced by some margin. Note that it takes more space even when the tag names are smaller.

Empty white space in the dialogue boxes

There is white space above and below the tags. This can be removed a bit to reduce redundant space. This space is not present in current design. Some space can be saved by doing.

Can this be implemented?

feature-request status-completed

The feature is still called 'favorite tags' in some places, like the Help Center:

Add favorite and ignored tags

Another way to filter out questions you're not interested in and focus on the ones you do care about is to add favorite and ignored tags to your account.

Favorite tags are meant to call out questions that are important or interesting to you. Any question tagged with one of your favorite tags will be highlighted on the homepage and questions lists.

(while you're at it, please update the screenshots as well)

Another example is further down the page, which also mentions a non-existing star icon:

You can also toggle a tag between normal, favorite, or ignored by mousing over the tag and clicking the star icon.

Also, the 'Favorite Tags' filter:

This came up on MSO and I thought it was a good idea so I'm reposting it here.

I'd go one step further than the OP's proposal, and remove the entire tag description block. We don't need this on every single page, forever! Who really needs a tag description permanently cluttering the space?

If we made the [Python] clickable or hooverable, that'll amply do.
The watch/unwatch/ignore/nore is already on the right side bar, it is not necessary there. Surely, there must be other, & better ways to induce people's goodwill to edit and improve tag definitions.

Notifications regression

Before this change, I could subscribe to a tag to get email notifications for new questions (after 15 minutes, 3 hours, or 1 day) by clicking this link:

This link has now been removed, to be restored in some way at some time in the future, per the question. This isn't a case of not-yet-met plans for future functionality; this is something that used to be available, isn't now, and is promised again for the future.

The only thing I use tag favorites for right now is to get email about new questions in them. Can I still do that somehow? If not through the UI, then how? That "subscribe" link in my screenshot isn't a direct link; right-clicking on it in my browser doesn't offer me "copy link address" so I can get something to inspect.

I don't see the link "Add an ignored tag" when I unignored my last tag.

It is back after refreshing a page.

Also, the "edit" button doesn't disappear when there is nothing to edit.

Could we have the "View tag" button more prominent?

Instead of:

We could have an easier to find "View tag" (forgive my poor GIMP):

Style is up to you: I just want "View tag" as big as the other options.

And if the size change isn't approved, could we instead adjust the position of "View tag" and "Watch Tag" to the right of the popup, for accessibility for right handed people?

I'm unable to watch or ignore non-existent tags

This probably explains something I noticed the other day, I'm no longer to watch or ignore tags that do not exist (yet).

Rationale

Why would I want to do that? The answer lies between those parentheses. I want to be able to add tags that don't exist yet, but that I expect or hope to exist in the future.

Example

My home stack is Science Fiction & Fantasy. Let's say a highly anticipated new film is coming out, for instance a new Star Wars film. No questions have been asked about it yet, but the title is already known, so I know what the tag will be. I want to avoid spoilers as much as possible, so I want to ignore the projected tag. But now I can't do that any longer, since I can't ignore tags that do not exist!

Another example would be following a tag of a favourite author about whom no questions have been asked yet, but I expect there aren't as many users having that same issue.

Don't silently alter my existing tags, either!

Additionally, I noticed that older non-existent tags had been silently removed from my list of favourite tags when I edited it to add another tag. I noticed and backed out without saving. Please don't do that.

If one box gives me the option to "Watch a tag" and explains what that will let me do, the other one should let me "Ignore a tag" and explain what the consequences might be. (Honestly, I'd like to know.) The wording "Add an ignored tag" is super geeky, at best. Add it to what? Tomorrow's soup?

I don't know what a notification might be, but I'd like to see a little marker beside the watched tag indicating that there is some unseen activity. And ideally, I'd like it to show up immediately, or a reasonable approximation. That's somewhat like the old new-nav tabs, except that the indications on those tabs were too fragile; they vanished on refresh. I'd like it to be like the markers on messages/rep: the marker stays until you act. Other than that, I was pretty fond of the nav tabs so I'm looking forward to getting something like them back.

So... I actually find the new name more confusing.

Favorite tags - by definition, is a list of tags I like. (Which is what it was)

Watched tags - by definition, is an activity. I am actively interested in these tags. So why can't I actively follow multiple tags at once? (Or am I just not seeing this feature? The closest is the "interesting" question tab, but that is clearly ignoring my watch list) Not counting notifications because that's mostly passive. (And not a feature yet)

I don't like the idea of the coming notification feature... I am only interested in new questions for ~1 hour after they are posted (After that, they are either well answered, or require very specific knowledge). I'd have to experience how the notifications work, but if they are normal notifications, I would expect to be flooded by notifications I no longer care about if I take a short break from the site (filthy casual me!)

I would expect to be able to view "watched tags" in a question que (like the "New", "Unanswered", or "Interesting" tabs), because that is the closest behavior to "actively watching". I'm not flooded by pointless notifications if I take a week hiatus, and I can view questions up to however old I want, whenever I want.

(Please correct me if I'm wrong, but isn't the only thing watching a tag does right now is provide you a shortcut to filtering on that tag alone? Where is (if there is) the view all shortcut?)

One thing that doesn't quite make sense to me, is:

I click on a Watched Tag to show the newest questions with that tag. The top of the page then looks like this:

I get buttons to "Unwatch Tag" and "Ignore Tag". Why would I want to ignore it if I'm watching it? How can I watch it and ignore it at the same time? You mentioned something about a tristate link previously, but maybe that was more sensible/clear? I am unlikely to ignore a tag until after I have unwatched it, after all.

And related: from this page, "Unwatch Tag" shouldn't be as prominent as it is an action I am not all together that likely to take compared to just editing my watched tags list.

Two nitpicks:

1. After pressing 'Edit' in the top right of 'Watched Tags', there is no way to revert back back to the previous state. Perhaps there should be a 'Done' button.

2. The highlight around the text fields ends abruptly on the right hand side:

In my opinion it should match the style of the top search bar, which gets a faint all-round drop-shadow

Watch tags to curate your list of questions and receive optional notifications on that tag's activity.

There is, of course, the tags/tag's issue that nitsua60 has already dealt with admirablely. But the rest of the sentence contains some peculiarities as well.

to curate your list of questions

I have a list of questions that I am, moreover, curating? When I go to stack overflow.com, I am presented by a list of questions called "Top Questions". I can't say I've ever thought of them as "my questions". Right now, the top question deals is one tagged 'xamarin' -- which as far as I know is a kind of fruit. Have I 'curated' this list by setting 'cocoa', 'xml' and 'xcode', among others, as my Watched tags?

As I understand it 'curate' has been gaining in popularity since museums started using it in their marketing, as in: a new exhibition curated by Hatsuko Mpufu von Schtottelheim-Chomborley. Which means that Hattie had a good look around the basements and picked some stuff. However, by watching a tag, I'm not really assembling a collection of great questions, am I? I'm just more likely to see some questions rather than others, regardless of their quality.

optional notifications on that tag's activity

Tags used to be labels, but now they've become actors as well? They're no longer the electronic equivalent of a hanger on a dog's collar, but they themselves go out sniffing for questions? Even metaphors get busy these days.

status-planned

This seems to have been rolled out without proper localizations.

For example, on the Portuguese version of Stack Overflow we read this strange English intrusion:

Similarly, on the Spanish version of Stack Overflow we read that same English intrusion:

Could we please get these translated properly on all the sites that have a native UI?

(The word “curate” there in the middle of it actually means something in those two languages, which threw me off a little. I kept thinking of how ¡Cúrate a ti mismo! is Spanish for the old adage of Physician, heal thyself.)

This seems to have somehow borked the Favorite Tags section on (some?) sites that haven’t changed to the new system yet.

On ELU, for instance, the section now looks like this:

Notice how the “edit” link is squished up against the header, which no longer takes up the full width of the section. For comparison, the Hot Network Questions section right underneath it still looks correct:

Font size of "edit" is too big

The font size of "edit" should not be bigger than the tags below. This would be consistent with the "edit" links for questions and answers which are also set in a smaller font size.

The colors are off

The questions containing a watched tag are highlighted, but that highlighting (at least on Judaism.SE) is very dull and is very hard to distinguish from the other questions.

It should at least be similar to the coloring of the 'Featured' sidebar, as it is on other sites (image taken from above answer):

Another thing, although this may be a little nitpicking, but I think the highlighting (notice the blue highlighting around the radio button 'Gray out questions in your ignored tags' in the first image) should also be consistent with the site coloring.