Continuity mistake: When Millhouse is being chased outside by a sun ray, the ray burns the pavement. It then turns around, and the pavement is now no longer burned. (00:01:40)
Continuity mistake: In the beginning, at the hospital, Maggie's bow changes from red to blue when Marge says "Why are you doing that?"
Continuity mistake: In the dinner scene at the end, Maggie is not wearing a bow, but when everyone tells Moe "Merry Christmas", she has her bow on.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.