Continuity mistake: When Krusty is telling his daughter that he lost her violin, keep an eye on the door of the appartment. A grey bar appears and disappears on the door underneath the "eyeglass" between shots.
Continuity mistake: After Amy Tan shames Lisa, there is a shot of Lisa wearing a red necklace, her necklace becomes her usual white one, seconds later.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.