Revealing mistake: If you look carefully in Mr. Burns' surveillance cameras, the workers are identical. (00:02:50)
Revealing mistake: When Smithers makes Mr. Burns his Wine Spritzer, Burns makes Homer Employee of the Month. While Smithers is pouring the stuff in the bottle, his left hand turns black for three frames. (00:10:30)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.