The Ziff Who Came to Dinner - S15-E14
Factual error: When the SEC guys break up the poker game they arm their guns in the same manner you would with a shotgun (there is even the shotgun cocking sound effect) yet they are M-16 style weapons and would not need to be armed this way.
The Ziff Who Came to Dinner - S15-E14
Continuity mistake: In once scene, Artie walks past the Simpson's to Selma (or Patty). In the next shot he is shown walking past the Simpson's again.
The Ziff Who Came to Dinner - S15-E14
Continuity mistake: When the Simpsons first see Artie Ziff in the attic, as he stands up, there's a theremin behind him (corresponding with Homer's comment that the "ghost" was playing his theremin). Artie puts a sign up above it. However, when Artie moves to the rafters, the sign he put up is still there, but the theremin isn't.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.