In the film The Moon of Earth, American Democrat Adlai Stevenson II appears and says he has no objection to men walking on the Moon. Stevenson being referred to as "Democratic hopeful" is because the filmstrip is so old that the 1952 presidential election still has not taken place. Additionally, his uncharismatic demeanor in the clip is a nod to Stevenson's own demeanor, which led to the term "egghead" being coined to describe him.
The scene where Bart gets bounced back by the excessive-decibels shockwave is similar to a scene from Back to the Future where Marty McFly uses Doc's gigantic speaker and super-amplifier with his guitar.
Bart thinks his parents are taking him to Disneyland.
The firing range scene is similar to the rifle range scene in the 1987 war drama film Full Metal Jacket.
When the Drill Sergeant tells Bart he missed his last target, Bart answers, "Did I?" This is a parody of the 1979 spy film Moonraker, when James Bond apparently misses a bird but actually shoots a sniper aiming at him.
During his call with Lisa, Abe talks to her about Admiral Byrd reaching the pole in 1934. In 1934, Admiral Richard E. Byrd spent five winter months alone in a meteorological base in Antarctica, where he almost died.
"The Eliminator" shares its name with the final event on the 1989 competition program American Gladiators.
When Bart tries to teach Lisa to cross "The Eliminator" at night, one of the cadets confronting him is dressed like James Dean from Rebel Without a Cause.
The same cadet plays "Taps" when it is Lisa's turn to cross "The Eliminator."
After Lisa passes "The Eliminator," she says she can't put her arms down. This is a reference to Randy Parker's "I Can't Put My Arms Down!" scene from the 1983 film A Christmas Story.
When Lisa looks down from the Eliminator, the platform under her disappears.
When Bart is driving a lawn mower and is pulled over by the police, Chief Wiggum is driving one of the police cars, even though he is inside telling Homer and Marge about sending Bart to military school.
During Bart's megaphone prank, a tan building turns blue for a frame.
When driving to Rommelwood, the car is Homer's Pink Sedan. However, upon leaving, it is the Orange Station Wagon. Later on, when Bart and Lisa graduate from the academy, they leave in the Orange Station Wagon. On the road, it is the Pink Sedan, however. Later, when it turns out Homer and Marge were taking them to the dentist rather than Disneyland, it's the Orange Station Wagon again.
Even though all the glass in Springfield breaks after Bart's megaphone prank, the glass in Chief Wiggum's patrol cruiser and Homer's car, as well as Professor Frink's glasses, stay intact.
