Eat My Shorts is a horse running in another race (and another of Bart's catchphrases).
There is a large drum of nuclear waste seen in the basement of the Simpson house in this episode.
Bart's forgotten permission slip can be seen (just barely) under his pillow before he wakes up at the beginning of the episode.
While imprisoned, Bart's cellmate is a seriously pumped-up Sideshow Bob. Sideshow Bob does not speak in this episode, presumably because he may be contemplating how Bart, who got Bob arrested in Krusty Gets Busted, is now an accused lawbreaker himself.
During the final scene the Simpsons watch a movie based on this episode. When the narrator lists the actors, the actor voicing Fat Tony is Joe Mantegna, who provides the voice of Fat Tony on The Simpsons.
The producers attempted to have "Be My Baby" by the Ronettes play midway through the episode. Due to being unable to secure permission, they used "One Fine Day" by the Chiffons instead. Be My Baby was famously used in Mean Streets, Martin Scorsese's breakthrough film.
On the news, Fat Tony's real name is revealed as "William "Fat Tony" Williams" but would later change to "Anthony "Fat Tony" D'Amico" in "The Homer They Fall," although the different names could be aliases, as Fat Tony is a mob boss and would need fake names to keep law enforcement off his tracks.
One of the rumors of Skinner's assumed murder is that the cafeteria made his corpse into hamburgers. In "Treehouse of Horror V", many Springfield Elementary students would be turned to food to solve the school's problems with overcrowding and budget cuts to the lunch program.
The footage of Smithers showing Mr. Burns the newspaper headline about Bart is recycled from Brush with Greatness. The scene where Marge is stirring her coffee with a concerned look on her face is also a recycled scene taken from Lisa's Substitute.
This episode takes several plot points from the film Goodfellas. Bart serving drinks to mobsters and abetting the gang by storing hijacked cigarette shipments was a reference to the rise of Henry Hill as a juvenille delinquent. The difference in the film is that Henry Hill was arrested for reselling the stolen cartons of cigarettes, whereas Bart naively assumed Fat Tony was a tobacco salesman.
Psychic Princess Opal's line, "I'm afraid it's splitsville for Delta Burke and Major Dad" is a reference to then-tabloid fodder Delta Burke and her husband Gerald McRaney. At the time of the episode, they were newlyweds, and a likely prediction that Hollywood marriages fail. However, the couple has remained together as of today.
In this episode Seymour Skinner is shown as having his own house, but later in the series he is shown as living with his mother. Later on he could have moved in with her, or vice versa.
In the scene in which Edna Krabappel is grieving over Seymour Skinner's absence, among the students who are there, Becky, is seen wearing green instead of the usual turquoise. She could've chosen to wear green that day.
Bart is shown bruised and his clothes ripped throughout the misadventures of his bad day. However, by the time he is inside the Legitimate Businessman's Social Club, he has no scrapes nor bruises, and he is now wearing intact clothes.
Bart is imprisoned with Sideshow Bob. Juvenile offenders are never jailed with their adult counterparts. In fact, later episodes even establish Springfield has juvenile detention centers.
Why didn’t Bart just ask Marge or Homer to drive him to school after he missed the bus instead of walking there which made him come late?
Bart walks to the school in the rain but later is shown riding his skateboard when he leaves.