I regularly find myself in a situation where a mistake creeps in a comment I made, and I realize it after the 5 min allowance is over. Perhaps I messed up a word, a formula, or some part of a link. When that's not disruptive (including, when that's in the last comment), I post a new comment and immediately remove the old one. But sometime that's unadvisable; I either leave frustrated, or on occasion I make a comment on my error (adding to the clutter), for it is not unheard that a moderator is kind enough to fix the mistake, and remove the comment about it.
I wish I had an edit one's comments (read "edit my own") privilege (perhaps coming with a badge). I think it should be awarded after some time/level of participation, or purchasable against a lot of rep. It should come with instruction to use it only in ways that can't change the meaning of a later discussion, and revocable if that's violated.
The only drawback I can see is that it will diminish the motivation to become moderator. But in my case, I don't want that privilege, for I have more than my share of tough decisions to make.