I'm Goin' to Praiseland - S12-E19
Revealing mistake: In one of the scenes (I think it is when they first discover the alleged 'miracle') you can see people in the background walking out of the park. But they are not walking out of the park at all, they are walking into the wall.
Revealing mistake: When Lisa wraps herself in Marge's arms right before she falls asleep, the inside of her mouth turns yellow.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.