Continuity mistake: Just before Marge tries to sell Skinner the tie rack, she is writing on something. She then puts her hands down by her waist, and then brings one up to turn it on and both up to pull the motor out. The point is that the pencil and the item she had in her hands have simply vanished, and we never saw her put them down either.
Continuity mistake: When George and Homer burst out of the manhole, there is a shot of the Simpsons' house covered in mud, then a quick one of it totally clean, then another when it's muddy again.
Continuity mistake: When Bart is looking for candy in the cupboards, the wine bottles in the nearby rack change position between shots.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.