Continuity mistake: While Lisa is standing in front of the table with her friends in the cafeteria, we see that the trays appear during the first shot, then after the camera zooms in on Lisa's table, the trays disappear. Then during the third shot, Lisa calls Alex over to her table. Look at the table again: the trays have reappeared.
Plot hole: When Bart locks Principal Skinner and Mrs Krabappel in Skinner's office, and tells them that they can't come out until they've reached an agreement, why didn't Skinner and Krabappel just climb out Skinner's office window instead of spending hours pounding on the door yelling to be let out?
Continuity mistake: In this episode Principal Skinner breaks into Bart's doctors office to find out if Bart has a 'kryptonite'. Bart discovered Skinner was allergic to peanuts. On Bart's medical history form under 'known allergies' it has shrimp ticked (they later battle with shrimp and peanut on a stick). However in a previous episode (The Heartbroke Kid, season 16 episode 17) it was discovered that he was allergic to cauliflower, so that should have been on the list as well.
Plot hole: When Bart prank-calls Moe and tells him his name is Jimbo Jones, Bart says that he lives at 1094 Evergreen Terrace instead of 742 Evergreen Terrace, where Jimbo and Bart are. If Moe had taken those directions, he wouldn't have arrived at the house, instead he would have gone somewhere different.
Other mistake: When Ned Flanders is calling Marge and Reverend Lovejoy from the Leftorium, he says that the three hooligans are in the shop on their motorbikes. But a few minutes before when Ned goes outside the shop to tell the boys to clear off, their bikes are nowhere in sight.