The issue with edits is the sort of situation where A tweets something B supports/likes so B retweets it, then A edits the tweet and puts something B would not want to boost in. What should happen to B's retweet?
The best option I can think of for edits is to have the edit just delete the original and give you an input field with the text, attachments, and replied-to fields filled in already. (Maybe do something fancy and skip reuploading large media that doesn't get changed.) As far as likes/links/retweets go it's an entirely separate tweet.
That or adding support for a reply to be flagged as having corrections and be promoted to the top of the reply list and somehow highlighted to bring attention to to.