At present, truly rude or offensive comments can be deleted by the community with a single flag if they contain particular words or by a group of flags on the same comment. These comment deletions occur instantly, and don't involve a moderator.
In fact, moderators aren't even notified when such comments are deleted. This means that the most hateful, disgusting comments can be posted, deleted, and no action taken on the user responsible. For example, these comments were recently posted to an answer and one-by-one automatically deleted with a single flag (warning, language):
No moderator saw any of these flags, or had any idea this exchange had happened. It was only hours later when we saw a custom flag calling attention to this that we were able to review the comment history, see this nasty exchange, and suspend the user responsible.
Terrible comments like this are posted regularly on Stack Overflow and quietly deleted. We can now see someone's history of flagged comments in their profile, but something else has to draw our attention to that. If an abusive user isn't pointed out to us in a custom flag or in other comment flags, they can keep posting ugly comments for a while.
Moderators need to know about deleted comments like this immediately so that we can deal with the user responsible. I propose that the system create an automatic moderator flag on non-moderator deletion of comments via flags, perhaps on the second such deletion of a comment. Automatic flags on deletion of a single comment might be too noisy, but if multiple comments are automatically deleted for a user we probably should know about that.
Such a flag might look like:
multiple rude comments (auto):
[You're an idiot](link1)
with the above Markdown rendered inline as we see for the "possible vandalism: deletions (auto):" flag at present. The links would be to the deleted comment, to provide us context.
This request is possibly a duplicate of my older request here, but this is specifically focused on comment flags. This has become enough of a problem that I wanted to suggest something more specific for this particular problem.