I actually disagree with the edit button for this very reason. One thing that Facebook (and DU, of all places) do is allow you to read the original content of any post that has been edited.
Often I wish FR had an edit feature, mostly so I could fix typos, but it has a preview feature so, really, all typos are my own fault. Ultimately, the lack of an edit feature preserves the integrity of the forum.
I do think that we should be able to self-delete posts, as every other forum will allow you to do. However, the mods here have always been receptive whenever I've asked them to delete a post of mine for whatever reason.
It's a public record so there shouldn't be an edit button.
If they're going to use one, when a tweet is edited, it should include a notice saying it was edited with a time stamp of the original and when the tweet was altered.