Here are some random tips from a recently retired MathOverflow moderator who spent a lot of time thinking about tags. Much of it tries to give a general answer to the question but I added some random thoughts and tips for eventual moderators along the way.
Tags that are adjectives are part of the broader class of meta-tags.
Do not use meta-tags in questions. Here are some tips to help you determine whether a tag is a meta-tag:
If the tag can’t work as the only tag on a question, it’s probably a meta-tag. Every tag you use should be able to work, more or less, as the only tag on a question. Meta-tags, like [beginner], [subjective], and [best-practices], are not helpful by themselves – they do not communicate anything about the content of the question.
If the tag commonly means different things to different people, it’s probably a meta-tag. For example, the meaning of the tag [subjective] is, itself, subjective; the same is true for tags like [best-practices] and [beginner]. Best practices to whom? Beginner by what criteria? Use only tags that have a broadly accepted, objective definition.
— From: proofassistants.stackexchange.com/help/tagging
We have a few meta-tags on MO, most are only there for historical reasons and still fewer are actually useful for users. It's still best to avoid them entirely. The very few that are actually useful will become obvious over time.
Overly broad tags should be nipped in the bud if possible. The reason is that they are often used as a catch-all for more specific and more appropriate tags, especially by novice users. Because there are many of these more appropriate tags, it's impossible to fix these using bulk actions. It's a nightmare to deal with these once there are a few hundred mistagged questions. It took years to deal with [algebra] and [geometry] on MO!
One thing that helped in the early days of MO was to have an initial list of top-level tags. Anton created tags for each math arXiv section on day 1 of MO. That led to a lot of debate over the years but it did help steer and organize the top-level tags.
Thing that are good to remember but many users fail to grasp initially:
Tags are not content and they are not classification tools. Tags are designed to bring attention to a question. Tags should be keywords that an expert is likely to look for. If you can't imagine anyone using the search bar for a word then it is not useful as a tag!
Also remember that people do read the title of the question. In fact, in most circumstances, users will read the title before looking at the tags. So it is always more important to pick a good title than to pick good tags.
