Continuity mistake: When the door is answered to Mr Burns and Mr Smithers, Barney is seen answering, who has orange sleeves. However when the door is opened, you can just make out a white sleeve, which could be none other than Homer's.
Continuity mistake: In the cafeteria scene where Milhouse shoots a spitball at Kearney, in the shot when Milhouse says, "We have order, but at what price," Milhouse, Lewis and the bullies all change positions at their tables. You may have to watch this part several times to understand it.
Continuity mistake: As Bart is on the phone trying to book his new act, you can see there is a split down his white shirt. When the shot changes and he tells Lisa to be quiet you can see that split has disappeared.