Audio problem: When Bart's gang is singing their song and Nelson is playing the banjo, he sings "because she's dead" and plays different notes yet his hands don't move along the neck of the guitar.
Other mistake: When the Amish are building the tree house, the top of the tree is missing. It's just sky. In the next shot the top of the tree is back.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.