Continuity mistake: Just after Homer has used the proton accelerator, Dean talks to him. In this scene he is writing something on a piece of paper, but he writes on the same line every time. He finishes writing on that line, then starts on it again.
Continuity mistake: The colour of the alien poster in the nerds' room changes from pink to blue.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.