Revealing mistake: When Homer pushes over the windmill something comes off and chops the head off a metal figure, but the head comes off before hit. (00:16:05)
Revealing mistake: When Marge stands up at one point in the airplane restaurant, her legs and part of her dress have disappeared.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.