Homer runs out of the house naked (with Lisa yelling at him to hide his shame and Ned playfully claiming that he could see Homer's doodle, which Homer responds with "Shut up, Flanders."), but when Homer finally picks up Bart from soccer, he has his clothes on (He could've went back into the house and changed, but it's not likely). Despite his stupidity, Homer does have occasional moments of brilliance. He may have stashed a change of clothes in the car during one of his "smarter moments" to prepare for this.
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 mistakenly in navy blue (although it is normally a light tan).
The R-rated movie that Milhouse, Lewis and Richard are so excited about seeing is Barton Fink, a 1991 drama about a struggling screenwriter in the 1940s, which presumably is far from what they would hope to see.
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 later parodied in "The Shinning" segment in "Treehouse of Horror V".
The woman that Bart mistakes for Homer in an ironic touch 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 of 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 by demanding, "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 [wikipedia:Who's Afraid of Virginia Woolf? (film) Who's Afraid of Virginia Woolf?] when 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 watches "Tuesday Night Live", which is 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 castmember on the show from 1980 to 1984. Bart's line about how he misses Joe Piscopo is also a reference to how most SNL viewers complain about the quality of the show (or will stop watching the show) 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 criticisms of Saturday Night Live's recurring sketches and characters being 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 comedically 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 that was shown here wasn't actually a clip from the actual show, but a parody that was animated by the Ren & Stimpy animators, including John Kricfalusi. Also, instead of Billy West voicing Ren & Stimpy, Dan Castellaneta voiced both of them for this parody.