Audio problem: When Bart's dog is chewing on the TV remote, one of the shots on it is of "I Can't Believe They Invented It." with Troy McClure as the host. This is exactly the same shot from "Homer vs Lisa and the 8th Commandment". You can tell because Troy's voice is different. The lip sync is also out, revealing that the line "As an actor, my eyeballs need to look their whitest" is dubbed in.
Continuity mistake: When Martin tells Bart about the answers being worthless, Bart is stood by the grass or the kerb depending on the shot. (00:04:00)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.