New Coke - When Herb commiserates with his fellow bums about losing his car company because of the car that Homer designed, he says, "Forbes called it the blunder of the century. A bit overblown, don't you think? What about New Coke?" At this, one of the bums protests and says he was the inventor of New Coke.
When Joe Frazier announces that Homer is the winner of "The First Annual Montgomery Burns Award For Outstanding Achievement in the Field of Excellence," the orchestra plays The Simpsons Theme.
2001: A Space Odyssey - When Homer has the furniture store salesperson demonstrate the Spinemelter 2000 vibrating chair on full power, the light show he experiences and his face being under different colors of light are exactly like the movie's penultimate scene.
Raffi was referenced when Herb demonstrated his Baby Translator, with one of the translations being "Turn off that damn Raffi record!".
The Wizard of Oz - When Herb gives gifts to the rest of the family, Homer (whose fondest wish was to have the Spinemelter 2000) dejectedly comments, "I don't think there's a vibrating chair in that bag for me." Near the end of The Wizard of Oz, after the Wizard gives gifts to the Scarecrow, the Lion, and the Tin Man (a diploma, a medal, and a testimonial, respectively), Dorothy—who wants only to go home—sadly says, "I don't think there's anything in that black bag for me."
The vibrating chair can be seen in the attic in later episodes.
Surprisingly, for such a revolutionary device, the baby translator is never seen again.
Originally, Barney Gumble was going to win in his fight against Joe Frazier, but Joe Frazier's son objected to that idea (as Frazier was a world champion at the time of the show's airing), so they changed it to Frazier winning.
Originally, Bart's line before he vaulted over the couch was "I do this for the Soviet Union!" However, the Soviet Union already broke down between the writing of the script and the air time, so the line was changed to "I do this for StainMaster Carpet, proud sponsor of the Living Room Olympics!"
George Foreman was originally supposed to be in the episode instead of Joe Frazier, but Foreman was unavailable.
The waiver that Mr. Burns has Homer sign became a law school discussion topic. In real life, if Homer had later discovered he became sterile due to his employment at the Springfield Nuclear Power Plant, he would have still been able to sue. Burns did not specifically state that Homer was sterilized or that the $2,000 was compensation for his having been sterilized. Instead, he called Homer "you big virile son-of-a-gun" and referred to the $2,000 as an award. That would be considered deception, so Burns would still be vulnerable to being sued—both for Homer's sterilization and for with holding that information from him. However, it's possible that the information was included in the contract as he didn't actually read it.
The reason why Homer wants the vibrating chair in the first place is because the couch broke. However, when Herb presents the baby translator to the family, the couch is intact. It's possible that Herb fixed the couch offscreen.