Comment flags are an interesting case to deal with. We often run across a single comment that was flagged as "not constructive" - possibly the most vague flag in existence. It's often difficult to tell how the comment is not constructive just by viewing only that comment. They oftentimes (especially on Meta) are replies to another comment, and there's probably another reply or more that comes after it. If this comment really isn't constructive, that implies that the rest of the conversation might not be either, or deleting it would break a conversation. So the only real way to diagnose this is to view the entire comment thread.
For small threads of comments, this isn't so bad, but sometimes when you visit a question and you see the "add / show {some huge number} more comments" button there, it's kind of depressing. You have to go through the trouble of figuring out where in that long thread the comment that was actually flagged is located. It is listed again at the bottom of our screen, but shows the same way as it is shown in flags queue.
My proposal:
Just plain don't show flagged comments in the overview at the bottom. Instead, link to the post as normal and indicate how many comments are currently flagged on that post. This makes that overview box smaller so there's more room to view the comment thread on the actual screen where I'm going to be looking (in those events where multiple comments got flagged throughout a conversation).
Add a dismiss button next to the delete button (directly in the comment thread) for the flagged comments. We can already edit and delete a comment directly in that comment thread, so that's the only piece we're missing since it only applies when a comment has been flagged.
Highlight the flagged comments somehow, perhaps in red, to make them stand out from the other comments. That way we can view the entire thread and see exactly where the flagged comments are located without having to read through every single one (they may not all be related) or trying to use the browser's find feature to locate them.
Automatically expand the entire comment thread on page load when there are flagged comments within it, to emphasize that the moderator should take action on them. The flagged comments may not be visible at first with the normal way comments are collapsed. It also seems like it'd be easier to highlight them once rather than maybe highlight them at first and then highlight them again when they're expanded.