Other mistake: When Bart, Lisa and Milhouse run away from the others, Lisa steps right on a puddle but no splash or ripple is made.
Other mistake: When everyone is eating the boar at the end, the boar is completely intact, yet everyone except for Lisa is seen with a piece of it. (00:20:30)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.