In the opening scene, Maggie spells EMCSQU with her blocks, a reference to Albert Einstein's mass-energy equivalence equation. A picture of Einstein also appears on the wall of Dr. Pryor's office. At one point Homer erroneously refers to Einstein as the inventor of the light bulb.
Dr. Pryor compares Bart's proposed work among ordinary children to Jane Goodall's study of chimpanzees.
The conductor of the opera the family attends is named Boris Csuposki, a reference to animator Gábor Csupó. The opera attended by the family is Carmen, by Georges Bizet; the song Bart mocks during the overture is the famous aria called the Toreador Song. The aria is later sung by "the bullfighter". Oddly enough, he doesn't sing it in French.
The Simpsons are playing Scrabble at the beginning of the episode.
Homer banging on Bart's locked bedroom door, yelling at Bart to open it, a reference to the closing credits of The Flintstones where Fred is banging on the locked door outside, yelling at Wilma to open it.
There is a picture of Bart on the wall opposite one of Albert Einstein in Dr. Pryor's office.
After Bart comes home green Homer washes him in Turpentine.
Homer thinks it was Albert Einstein that invented the light bulb.
When the Simpsons are playing Scrabble, Homer is complaining that he has not good letters; his slate of letters shows "O-X-I-D-I-Z-E", which is the highest word score one can achieve in Scrabble by using seven letters.
Martin Prince is the train conductor when Bart is told to visualize his IQ problems.
Bart wears a pink shirt to his first day of class at the "Enriched Learning Center for Gifted Children". Homer later (unintentionally) does this same thing in a future episode.
Books on the shelf in Bart's new advanced school classroom include Crime & Punishment, Babylonian Myths, Paradise Lost, Moby Dick, Plato, Dante's Inferno, The Illiad, Design of Computers (remember this is 1990), Astrophysics, Wana by Emile Zona, Puskin, Shakespeare I-XV, Quantum Mechanics, and the Life of Leonardo.
The Simpsons attend the opera "Carmen", advertised as "Tonight Only in Russian."
On the opera poster, the conductor is identified as Boris Csuposki, a reference to the name of producer and supervising animation director Gábor Csupó.
After he is dubbed a genius, Bart's Principal Skinner graffiti is framed and labeled as a work of art entitled "The Principal" by Bart Simpson.
Bart's word Kwyjibo is later used in Champions Online as the name of a super-powered gorilla. Here it's spelled with a Q instead of a K. It is also used in the demo version of the LucasArts game The Secret of Monkey Island, also released in 1990.
When Martin is telling Principal Skinner that Bart is spray painting the wall, there is a blonde girl in the background that resembles Lisa except that her hair is more spikey than Lisa's and is wearing a blue-green dress.
Homer comments to Bart that for generations Simpson men have dreamed of outsmarting someone. Homer does just that, by outsmarting Cooder in Bart Carny.
Someone suggests to Bart that he build a rocket ship. In She of Little Faith, Bart worked on a rocket ship.
Dr. Pryor explains that high intelligence is usually caused by hereditary. In Homer Loves Flanders it is mentioned that genetics are making Homer a loser. The Simpsons genetic intelligence was further explored in Lisa the Simpson.
In this episode, Mrs. Krabappel states that the IQ tests will have no effect on the students' grades and are merely a reflection of the students' future success, but in the Treehouse of Horror VI story, "Nightmare on Evergreen Terrace", she encourages the class to fail their latest standardized test because the school gets more funding this way.
Principal Skinner has a secretary and an intercom in this episode. In Who Shot Mr. Burns? (Part One), Principal Skinner says he doesn't have a secretary or an intercom.