Continuity mistake: When the "Angel" tells everyone to prepare for the end, Carl is seen with yellow skin.
Continuity mistake: While everyone in Springfield is waiting for the apocalypse, Dr. Hibbert's wife Bernice is seen with yellow skin while she's holding on to him.
Continuity mistake: When Dr. Gould says the DNA test was inconclusive, Apu is seen in the background with yellow skin.
Continuity mistake: During the scenes at the site of the mall during the part where they find the Angel, Skinner's hat disappears and reappears.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.