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.
Continuity mistake: After the boy's car gets crushed, Bart sells Milhouse's glasses for $600. Then Milhouse knocks over the Coke bottles and the clerk gets the money back and keeps the glasses. The next scene, where they try to get on a train that goes to Springfield, you can see Milhouse in his glasses and throughout the rest of the episode.
Continuity mistake: In the new opening sequence (season 20), you see Kearney and Jimbo sawing off the Jebediah Springfield statue's head, which starts falling down. In this wide plan, overhead and closing up, the whole town square is in full sight with no one visible besides those characters. The shot cuts to a close-up of the statue's head falling on Ralph Wiggum, now right next to the statue's pedestal where he was calmly eating an ice cream cone.