Moderators should be able to comment on things after normal users are unable to, such as when a post is deleted or locked. As a moderator on Programmers, I try to leave a comment (if necessary) before taking the appropriate action on the post. However, in the time it takes to write a comment (which often includes digging up links to the most relevant resources and citing specific problems), things may happen - users can leave new answers or comments, Community or the author can delete the post, and so on.
A responding moderator should be able to take the appropriate moderator action on the post to remove the problematic behavior/content from the site and then leave a comment so that the user can learn why this behavior is unacceptable or what needs to be done to fix the content (if it's fixable).
This would effectively change the workflow from {hope no one will do anything -> write a comment -> hope nothing happened to the post that invalidates or blocks the comment -> moderate} to {moderate -> comment}.
Diamond moderators should be able to comment on posts that are otherwise locked from comments.
When a moderator comments on a deleted post, the comment should generate an inbox notification for the post's author just as it would if it were posted right before the post was deleted.