Please check your access rules. I tested it with the last versions and there was no problems.
I don't have a clue why but I can't see any checkoboxes near uj_ajax_cart in rules table.
But what I fixed today is I put the module folder into ubercart/contrib (previously I just uploaded it to sites/all/modules).
After that, the uploading image ('Adding to cart') shows only when I'm logged, on FF. On IE & Chrome it works but shows button with 'Add to cart...Add to cart...' (exactly) when adding product to cart through Ajax.
jQuery Update 5.x-2.0
Ubercart 1.4
Thickbox 5.x-1.2
^ But now I see there's an update for Thickbox, I will try uc_ajax_cart with that new one.
