Homer runs out of the house naked (with Lisa yelling at him to hide his shame and Flanders playfully claiming that he could see Homer's doodle), but when Homer finally picks up Bart, he has his clothes on. (He could have went back in 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 entire series. Originally, Principal Skinner was supposed to wear a toupee and it was supposed to be a running joke, but Matt Groening thought toupee jokes were too cliched, and scrapped the idea.
The name "I.P. Freely" was previously used in "Homer's Odyssey" by Bart as a crank call to Moe. This time the call was made by drunken fraternity boys, who were the alleged sources to the fight of a giant lizard in Downtown Springfield to Kent Brockman.
The shot of Homer saying "Marge, when kids say 'bad' these days, they mean 'good'. And to 'shake your booty' means to wiggle one's butt" is recycled from the opening scene from Life on the Fast Lane.
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!" he is making a reference to 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.
At one point, Bart tells Homer that he would fake the excitement he would have when Homer pushed him on the swing and demonstrates it, to Homer's horror. This is a reference to the infamous fake orgasm scene in When Harry Met Sally.
A section of the fight between Homer and Tom parodies the introduction to Street Fighter II.
At one point, Bart watches "Tuesday Night Live", which is a parody of NBC's Saturday Night Live. At a 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 12 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.