Well, are they really such big problems that you need to rewrite your post or otherwise nobody will understand? Also, it's not that much effort to recheck your posts before posting, is it?
The big problems with an edit button are that it's very open to abuse (e.g. posting nude/shock pics and removing them when a mod comes online) and it can cause a lot of confusion (the whole continuity of a thread is broken after people edit some of their posts). So I think it will create way more problems than it solves.