While on a day trip to a hands-on science museum, Marge feels sorry for Ralph Wiggum being bullied and suggests to Chief Wiggum that Ralph and Bart be play buddies, which Bart objects to — until he realizes that Ralph is the son of an incompetent police chief and has police equipment at his disposal (including a master key that opens up every lock in town — including one to an abandoned prison's electric chair).
- Brick Joke: Ralph mentions that he's friends with a leprechaun that tells him to burn things. In the end, when everyone is cheering for him, the leprechaun tells Ralph to burn down The Simpsons' house.
- A Day in the Limelight: For Ralph and Bart, mostly.
- Sarcasm-Blind: When Mrs. Krabappel asked the students seven times eight, Milhouse answered "low battery" (they were using calculators) and didn't understand her reaction to his answer was sarcastic.
- The Scrooge: Mr. Burns saved Mayor Quimby by cutting off the electricity supply to the electric chair, but his motives were less than noble. Burns simply wouldn't supply electricity to anyone who wasn't paying for it (though why would a prison still have electricity and a security guard if no-one's been using it for years?)
- Throw the Dog a Bone: Lisa was the one to come up with a plan to save Mayor Quimby but the one congratulated was Ralph for suggesting to ask for her help. Lisa gives in out of pity.