Editing posts was potentially dicey territory for Facebook, since the it brings the danger of a bait-and-switch with followers. A user could conceivably write, "Who likes ice cream?" and get hundreds of Likes and affirming comments, then edit the post to read, "Who wants to beat up some cats?"
Facebook addresses this issue by marking the post as edited and letting users access the history of any edited post with a click. Google+, which has let users edit posts for some time, works in a similar fashion.
Facebook has been slowly granting users more editing capabilities over their content. Users can edit photo captions (that is, status updates with a photo attached) and the ability to edit comments arrived a few months ago.