Chalkboard Gag: I will not waste chalk.

Couch Gag: The family rushes in and crams onto the couch. Bart pops out and comes crashing down seconds later in front of the TV as the opening credits end.

With the first real intro, we see Maggie worth $847.63.

This episode marks the first time we see Martin Prince.

This episode marks the first time we see Edna Krabappel.

At Bart's new classroom, there's a book called "Homer's Odyssey" which is the title of the next episode.

Maggie spells out EMCSQU, or E=MC², with her building blocks.

This is the first official episode, FOX says that Simpsons Roasting On An Open Fire was considered a special.

In the Season 1 DVD commentary for this episode, we learn that Dr. J. Loren Pryor was the original drawing for Principal Skinner. Skinner's current look is based around a few teachers and a principal Groening knew, as well as the principal from the "Life In Hell" comics.

In this episode we learn that Martin has an IQ of 216.

Mrs. Krabappel: What are you looking at, Bart? Are those naughty dogs back again?

Homer: What do we need a psychologist for? We know our kid is nuts.

Principal Skinner: Whoever did this is in very deep trouble.
Martin Prince: And a sloppy speller, too. The preferred spelling of wiener is W-I-E-N-E-R, although E-I is an acceptable ethnic variant.

Martin Prince: Bart, I hope you won't bear some sort of simple-minded grudge against me. I was merely trying to fend off the desecration of the school building.
Bart: Eat my shorts.
Martin: Pardon?

Mrs. Krabappel: Now I don't want you to worry, class. These tests will have no effect on your grades. They merely determine your future social status and financial success. If any.

Homer: Don't be discouraged, son. I bet Einstein turned himself all sorts of colors before he invented the lightbulb.

Homer: Phe-yew, when is this over?
Bart: It aint over till the fat lady sings!
Homer: Is that one fat enough for you, son?

Bart: My turn. Kwyjibo. K-W-Y-J-I-B-O. Twenty-two points, plus triple word score, plus fifty points for using all my letters. Game's over. I'm outta here.
Homer: Wait a minute, you little cheater. You're not going anywhere until you tell me what a Kwyjibo is.
Bart: Kwyjibo. Ah, a big dumb balding North American ape... with no chin.
Marge: And a short temper.

(Bart reads a math problem aloud from his aptitude test)
Bart: At 7:30 a.m., an express train traveling 60 miles an hour leaves Santa Fe bound for Phoenix, 520 miles away.
Mrs. Krabappel: Shh! Visualize it, Bart.
(Bart reads silently and pictures the story problem in his head)
Bart: At the same time, a local train traveling 30 miles an hour and carrying 40 passengers leaves Phoenix bound for Santa Fe. It's eight cars long and always carries the same number of passengers in each car. An hour later a number of passengers equal to half the number of minutes past the hour get off, but three times as many plus six get on. At the second stop, half the passengers plus two get off, but twice as many get on as got on at the first stop.
(Bart visualizes himself on the train as the passengers bump him around)
Bart: Oof!
Conductor: Ticket, please.
Bart: I don't have a ticket.
Conductor: Come with me, boy.
(The conductor drags Bart to the front of the train)
Conductor: We've got a stowaway, sir.
Bart: I'll pay. How much?
Martin the Engineer: Twice the fare from Tucson to Flagstaff, minus two-thirds of the fare from Albuquerque to El Paso. (Emits an evil laugh)

When Marge tells Homer to close his eyes and she takes the money jar out, her necklace is red. When she takes it out of her hair in the next shot, her necklace is white.

When Marge tells Homer that the Christmas money is gone, he is standing in front of the kitchen. But when the camera cuts to Marge, she is the one standing in front of the kitchen.

Gabor Csupo

An advertisement at the opera identifies the conductor as Boris Csupovski. This is a reference to Gabor Csupo, the Supervising Animation Director in 1990.

The Adding Machine

The dream Bart has while attempting to do the math problem is based on the play The Adding Machine.