We should be able to edit our posts like we can on Facebook. Even if there were a 5 minute time limit or something, it would be rather nice if one noticed that they made a typo or something and wanted to correct it quickly.
No because there is harassment on this site and moderators cannot always rectify it before the harm is done. It is important such things cannot be edited away because moderators would have an even tougher time protecting people.
Proof reading is your friend, as is not clicking 'Send It!' before you have proof read.