I already fixed this but I thought I would post this so others could find it.
I used the Members plugin to create a custom role for all the users using document-revisions.
Everything worked fine, but the upload frame always got stuck at "crunching..." But if you click "save all changes", everything works fine.
Turnes out, a async call to async-upload.php gets an 500 error.
This is because the file checks for the "edit_posts" capability.(http://core.trac.wordpress.org/ticket/8234 and http://core.trac.wordpress.org/ticket/21091)
So if you want people to have a good experience when uploading files, give the the right to 'edit_posts'.
This took me forever to find. Hope I could save anybody sometime.