Revealing mistake: When Lisa and Hugh go by Taxi to the Simpsons house, you can see that they pass the same buildings all the time, especially "Coffee shop".
Revealing mistake: By the end, when fortune teller lays "The Fiance" card on the table, it instantly makes the same angle as other cards lying there, even though the teller's hand is still under it. It doesn't change the angle when she removes her hand from under it, as though it's floating in the mid-air all the time.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.