At the beginning as Bart waits for Homer and the car arrives, Jimbo Jones is sitting in the back seat but nobody is driving.
The chalkboard gag, "The Principal's toupee is not a Frisbee", is the only mention of Principal Skinner's hair being fake in the show's universe. Originally, Principal Skinner was supposed to wear a toupee and it was supposed to be a running joke, but Matt Groening thought that toupee jokes were too cliched, and scrapped the idea completely.
Near the beginning of the second act, the shot of Homer saying "Marge, when kids these days say 'bad', they mean 'good'. And to 'shake your booty' means 'to wiggle one's butt' is recycled from Life on the Fast Lane where Homer says "But it's a surprise." This is due to Season 4 reusing lots of animation from previous seasons in order to save more money.
When Homer shows Pepihis house's garage door, "a wonder of modern technology," the garage door is navy blue, while it is normally a light tan.
Homer runs out of the house naked, but when he picks up Bart from soccer, he has his clothes on.
He could have gone back into the house and changed. Alternatively, he may have stashed a change of clothes in the car during one of his smarter moments to prepare for this.
The R-rated movie that Milhouse, Lewis and Richard are so excited about seeing is Barton Fink, a 1991 drama produced by 20th Century Fox about a struggling screenwriter in the 1940s, which presumably is far from what they would hope to see.
A later episode, "Bart the Fink," would take its title from that film.
Milhouse writes "Trab pu kcip" on the wall, which is "Pick up Bart" backwards, a reference to Danny Torrance writing "redrum" (which is "murder" backwards) in The Shining. This was parodied again in "The Shinning" segment in "Treehouse of Horror V."
The woman that Bart mistakes for Homer sings "I Am Woman."
While Bart is stuck in the storm waiting for Homer to pick him up, a nun is lifted up by the wind, a reference to the TV series The Flying Nun.
The grapefruit scene is a reference to the James Cagney movie, The Public Enemy.
At the beginning of the first act, when Bart tells himself, "Eye of the Tiger, Bart," during soccer practice, it is a spoof on what Rocky says to himself in Rocky III.
When Homer confronts Bart with, "You've been gallivanting around with that floozy of a bigger brother of yours, haven't you? Haven't you!" it is a reference to the scene in Who's Afraid of Virginia Woolfin which Richard Burton accuses his wife of adultery.
Skinner makes a reference to the movie Psycho when he says "Oh... there's mother now." This is the first time Skinner has been portrayed as a Norman Bates-like character.
During the third act, Bart tells Homer that he would fake the excitement he would have when Homer pushed him on the swing and demonstrates it, much to Homer's horror. This is a reference to the infamous fake orgasm scene in When Harry Met Sally.
Near the end of the first act, Bart watchesTuesday Night Live, a parody of NBC's Saturday Night Live. Before Tuesday Night Live goes to commercial break, Bart comments that he misses Joe Piscopo, who was a cast member on the show from 1980 to 1984. Bart's line about how he misses Joe Piscopo is also a reference to how many SNL viewers complain about the quality of the show (or will stop watching) due to a fan-favorite cast member leaving, quitting, or being fired.
Krusty appears on a sketch called "The Big Ear Family", which could be a reference to either the Coneheads or The Widettes, the Coneheads being a family of aliens with large cone-shaped heads, and the Widettes being a family of people with abnormally-large rear ends.
Krusty's line about how the sketch goes on for another twelve minutes, despite the very thin joke premise is a reference to the criticism that Saturday Night Live's recurring sketches and characters are one-note.
Krusty's line during the monologue about the last half-hour of Tuesday Night Live being a garbage dump is also a reference to SNL putting weaker, less funny, and more experimental sketches on after Weekend Update (which marks the last half hour of the show).
The fight between Homer and Tom mirrors a fight at the end of The Quiet Man, a John Wayne movie.
During the second act, Bart and Tom are watching The Ren & Stimpy Show on Tom's television. The Ren & Stimpy cartoon shown is not actually a clip from the show, but a parody animated by the Ren & Stimpy animators. Also, Ren and Stimpy are voiced by Dan Castellaneta rather than Billy West.
Although John Kricfalusi worked closely with Matt Groening in writing that parody scene, he was unable to do the animation or drawings as Nickelodeon's Games Productions took over the show's production at the time.