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. (00:11:25)
Audio problem: When Homer is talking to the family about their complaints about the nerds, he says something that ends in "where we can all live in harmony". When he says this the audio does not match his mouth movements.
Continuity mistake: The colour of the alien poster in the nerds' room changes from pink to blue.
Continuity mistake: When Bart runs his nails down the chalkboard, the image on the board changes slightly; note the legs. There is a gap between one leg and the body in one shot, but not the other. (00:14:00)
Continuity mistake: When reading his responses to college applications, Homer pushes his plate away, but as he stands up, an empty plate appears in front of him. (00:07:00)
Continuity mistake: Homer puts his photo on his application, and there is no white spot behind his head in the picture. When the shot changes, there is now a white patch in the photo. (00:06:00)
Continuity mistake: The writing on the entrance essay Lisa is reading changes between shots. (00:05:40)
Continuity mistake: Burns brings out the mystery box and places it on the desk. This box then simply disappears. (00:03:40)
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.