I think the concerns about an edit button are overblown, but there would be very little downside to Twitter having a “retraction” option, wherein the tweet is left up but with a strikethrough indicating it is not or is no longer valid.
This is a fantastic idea. How many times have you seen a tweet with tens of thousands of likes and retweets, only to be followed by a less popular self-reply correction? The current mechanism for modifying a tweet is clearly inadequate, and deleting an offending tweet means a record of the origin of some piece of incorrect information may be lost. Brilliant.