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.
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.