It is now possible to edit your facebook posts. There is a down arrow at the top right of each post made by you that has the text "Edit..." where you can change the text of your posts.
There's a new app available on Android that does this called Exfoliate. It exhaustively goes through all your friend's walls and deletes posts, comments, and likes.
Best Answer
Update 9/27/13.
Yes.
It is now possible to edit your facebook posts. There is a down arrow at the top right of each post made by you that has the text "Edit..." where you can change the text of your posts.