Popular forum software such as PHP and BB forum allows you to edit a post within, say 5 minutes of posting it, without marking it as edited. This is very useful for things like fixing typos, fixing markup (for example when you quote someone then delete some of their posting and accidentally kill one of the markup square brackets).
I want it on ST too 
Then, “edited by …” really means a true edit / change of mind later.
But people really do change their minds quite quickly as well. In other words, it’s equally as valid an assumption that ANY change should be noted. Have you never posted something only to wish you hadn’t immediately? I don’t really see the value in giving a short edit. The unedited post is not publicly available to anyone. So it’s not like anyone would know anyway.
I think that people ought to use the “preview post” button more often.