A feature like this has three main variables to figure out and any functional PM or company should be able to answer these questions and test the preferred options with users in a few weeks at most.
1) period of time a Tweet is editable for: a few mins or forever? As Tweets are retweeted by others and embeddable, making them editable for only a few minutes after they’re first posted seems like the best approach as users who are retweeting don’t want a Tweet to be able to be edited to have a very different meaning.
2) is the Tweet ‘live’ and able to be retweeted while it’s editable or is it only live after the Tweet is no longer able to be edited? I prefer the latter approach as it makes the implementation a lot easier and essentially maintains Twitter as it currently works.
3) how to indicate a Tweet has been edited - adding an “edit history” link to Tweets only if they’ve been edited and linking these to a page showing the edit history of the page URL in simple coloured diffs seems to answer this question.