Revealing mistake: While Patty tells Selma "Look who's talking" after Homer debuts his new haircut, both of their chests up to their necklaces are the same color as their dresses. Selma's dress also suddenly has sleeves on it.
Revealing mistake: When talking to the doctor about using his health insurance, Homer's hairline above his ear vanishes in a shot then reappears.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.