The one issue with an edit button is I find it really common to edit a FB post within 5 minutes of making it. Either because I noticed a typo, I decided to change my wording or tone, or I forgot that enter == submit.
But afterwards when a lot of people have read and even replied to it... I think edits should be labelled. Otherwise you just end up confusing people who clearly remember "a" but are now seeing "b".