The recurrence of the initials "DEI" in the movie is no accident. The truck that is used to transport the popcorn to Dr. Hathaway's new house has "Drain Experts Inc." emblazoned on its side. The company Chris interviews with at the beginning (and which funds Dr. Hathaway's show "Everything") is Darlington Electronic Instruments. The initials are rumored to have been inscribed by Caltech alumni at (among other places) the summit of Everest, on the moon and on many satellites and space probes manufactured at Jet Propulsion Labs (which sits just up the hill from Caltech in Pasadena). There has long been an unofficial contest to see who could place the letters DEI into the most prominent public view. Their placement in this film was with the full complicity of director Martha Coolidge and her Caltech advisor, David Marvit.
When Hollyfeld sends in a large number of entries to the Frito-Lay contest, he is mirroring the actions of Caltech students Steve Klein, Dave Novikoff and Barry Megdal, who, in 1974, used a similar strategy to win a McDonald's sweepstakes. Their entries came to roughly 1/5th of the total entries and won them a station wagon, $3,000 cash and $1,500 in food gift certificates.
The aircraft featured in the movie was a B-1B "Lancer". Today, a real-life analog exists in the United States Air Force's Airborne Laser (ABL) project, a collaboration with Boeing, involving a modified 747 cargo jet carrying a megawatt Oxygen-Iodine laser, whose purpose is to shoot down enemy ballistic missiles.
When Chris and Mitch enter the plane, a background technician speaks "Final check: latitude 65 degrees, 19 minutes, longitude 44 degrees, 09 minutes." These coordinates lie in Russia just below the Arctic Circle near the White Sea, which was a key Soviet, now Russian Federation, naval and submarine base.
The "liquid nitrogen" coins have baffled viewers for many years, and are considered by many to be a goof. However the very first draft of the script shows that it wasn't an error. The thermos contains liquid nitrogen, which in turn contains a column of super-cooled CO2 (dry ice), which is what Chris uses in the vending machine.
In earlier versions of the script the Potassium-Cyanide laser, not the Bromide-Argon laser, used frozen fuel. This is why Chris tells the laser to "stay cool" before he goes off to take Hatheway's exam.
The coordinates for Hathaway's house are given in the film as "34D 10M 15.21S NORTH, 119D 7M ..." Assuming the longitude is in the western hemisphere, that's somewhere in an area of farmlands east of Oxnard, California. The script gave a slightly different set of coordinates: "Thirty-four degrees, ten minutes, fifteen seconds North; one hundred eighteen degrees, nine minutes, three seconds West." The building at that location is a mortuary in Pasadena, a few blocks north of Caltech.
In 2010, actor William Atherton told "The A.V. Club" that the popcorn used in the final scenes was treated with a flame-retardant chemical and so the crew went to great lengths to guard it against being eaten by birds, which would have died from the contaminant. Atherton also said that even with a machine in the studio dedicated to doing nothing but popping the popcorn, it took three months to pop it all.
The writings on the walls in the steam tunnels ("light your way", etc) are references to the game "Wizardry" and its sequels, in which clues can be found scrawled on the walls of the dungeon. The ending credits contain: "Thank to Sir-Tech, for Wizardry". Alternatively, assuming that Real Genius is meant to represent Caltech, the writing on the walls of the steam tunnels could be representative of the real writing on the walls of the real steam tunnels at Caltech.
When Mitch rides the cart into the steam tunnels, the viewer briefly sees the quotation, "Against stupidity the gods themselves contend in vain" scrawled on the left wall. These are the original words of German poet 'Friedrich Schiller (I)'. Relevant to the film, Isaac Asimov named three separate stories "Against Stupidity", "The Gods Themselves" and "Contend in Vain". He later combined them into a 1972 science-fiction novel about a conspiracy by aliens who inhabit a parallel universe with different physical laws than ours, and who are trying to turn our sun into a supernova in order to collect the resulting energy for their use.