Continuity mistake: The bible that Reverend Lovejoy returns at the library is bigger in the first shot.
Continuity mistake: When Bart says "Everybody, come quick!", the fridge door goes from open to closed.
Continuity mistake: In this episode and maybe in other one, the door to the basement is at the entrance of the house, but that's a closet in other episode.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.