Considering that the comment text itself logically belongs to the user who posted the comment, but the title applies to all comments in the thread; who should have the ability to edit the thread title? Just the user who posted the first comment; any user who has a visible comment in the thread; or anyone at all? What if, say, the initial comment has been deleted? In that case, should a distinction be made between a self-deletion and deletion by another user (who might be a moderator)?

I say, the original poster of the comment should be the only one (unless it's a mod due to say, profanity); that said, I think that the original name of a comment thread should be it's only name unless changed by mod. I'll leave the matter of how do that for the community managers.