Continuity mistake: In the bit where they sit on the sofa at the start of each episode, there is one rather long one where it starts off with the Simpsons dancing in a line, then gradually evolves into a circus with elephants and men dancing around fire. Look closely in between Homer's right leg and the dancing woman on his right. There is a pile of books on the little shelf underneath the lamp and telephone, and just as the camera starts zooming out from the line of dancing, the orange book on the left noticeably changes to purple. (00:01:20)
Continuity mistake: Millhouse is in the classroom at the beginning when Principal Skinner says that superintendent Chalmers is coming for a surprise inspection, but when they show Nelson he is getting crud put down his shirt. How could he be at two places at once?
Continuity mistake: Homer is interrupted from praying by a nurse who comes into his room and says, "Ssh." However, when she says this, the door is closed, and it is only in the next shot where the door is open immediately and she is pointing to the NO PRAYING sign. (00:14:20)
Continuity mistake: When the flashback of Ned and Todd Flanders singing in the Simpsons' doorway, Homer says he could use a TV tray. Then it goes back to the present time and Homer picks up a beer from the TV tray which is next to the couch. The TV tray was never there at any other point in the show. (00:10:40)
Continuity mistake: When Bart and Lisa wake Homer and Marge up in the morning of the Duff Gardens visit, the kids are standing by the bed. However, when Marge throws the mouldy sandwich in the bin in the next shot and Homer collapses, the kids have disappeared. In the next shot, they are back again.
Continuity mistake: In the scene where Marge is talking to Bart's teacher, Marge is "punished" by writing lines on the blackboard. In the first shot of her doing so she has written the line 9 times, but in the next shot there are 11 lines. (00:05:10)