Continuity mistake: The shaving cream on Chief Wiggum's face disappears when Bart tries to confess about the phony kidnapping.
Continuity mistake: Chief Wiggum's badge is shown to disappear under his fat in one scene, but in the following shot of him the badge is completely visible.
Continuity mistake: When Bart goes up to his treehouse to write the kidnap letter, he throws his Murder 4 Life jumper out the treehouse entrance. Later, when Lisa finds the jumper, it is now on a tree branch as if he threw it out of one of the treehouse windows.
Audio problem: When Homer says "Burn the truth" after burning his pants, his mouth doesn't match what he is saying.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.