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.
- When they first enter the Knowledgeum, The Simpsons are introduced to the place by Troy McClure who warns them that their car might be subjected to repeated break-ins. Homer was the only one worried about that. After leaving we clearly see their car has broken windows.
- A Day in the Limelight: For Ralph and Bart mostly, meaning that Nancy Cartwright gets to talk to herself through 90% of the episode, as she also voices Nelson Muntz and Kearney.
- Getting Crap Past the Radar: When Mr. Burns says "There's a rocket in my pocket!", Smithers says "You don't have to tell me, sir."
- Karma Houdini: The bullies, as usual, suffer no repercussions for turning on Bart and throwing away Ralph's master key, last seen walking off to find huckleberries.
- Nose Nuggets: "I found a moon rock in my nose!"Bart: Houston, we have a booger.
- 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?)
- Shout-Out: The guns in the "Let's Make a Baby" game resemble the Millennium Falcon guns in Star Wars.
- Skeleton Key: Chief Wiggum has one, which is shaped like a skull, which opens every door in Springfield. Bart and Ralph steal it and get up to mayhem.
- 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.
- Too Dumb to Live: Quimby seems to be actively trying to kill himself killed with the electric chair.
- What Does This Button Do?: Bart presses the keyboard buttons on the visible computer despite Frink telling him to stop. It's done to the point the computer crashes and catches fire.