Revealing mistake: When Jay is at the post office looking for Kay, he's talking to him in the parking lot and Kay is sitting in a mailman's cart. Jay says something to Kay, and Kay punches him, but you can see that he didn't touch him, especially since Jay reacts to the hit a split second before it happens. (00:28:45)
Revealing mistake: When Agent Jay is in the yellow tent with Serleena's tiny ship, the view back at HQ shows a shot from a distance behind the ship of Jay holding the communicator he's supposed to be transmitting the video from.