When Marge turns on the radio the song playing is 16 Tons by Tennessee Ernie Ford.
While Bill and Marty say that they had played "Take This Job and Shove It", the ending to "16 Tons" was played instead.
The media sensationalism of Bart not getting an elephant is akin to the media circus that surrounded Sherman McCoy in Bonfire of the Vanities. A headline says "KBBL Cheats Straight A Student!" without bothering to see that Bart is hardly a serious student. The 1990 film had a reporter interviewing a teacher of one of the carjackers, who stated "At Ridell High, an honor student is someone who comes to class at least once and does not piss on the teachers, so he qualifies" which then turns into a sensationalist story of a "straight A model minority student" harmed by McCoy.
When Homer accidentally drives into a deer statue, Homer responds with "D'oh!", quickly followed by "A deer!" by Lisa and "A female deer!" by Marge. This is a reference to a song in the movie "The Sound of Music."
The Springfield Tar Pits are a nod to the La Brea Tar Pits in Los Angeles. During the DVD commentary to this episode, Matt Groening admitted that one night he saw a bunch of "punks" dumping an old shopping cart into the tar pits.
The scene where Stampy is seen peering into the Simpsons' house parodies the T-Rex peering through the jeep door in Jurassic Park. Also, Stampy is laying on his side after eating all of those peanuts is similar to the sick triceratops in the movie.
The Mr. Cleanser cleaning solution and it's mascot that Homer uses in the basement are a parody of the real life cleaner, Mr. Clean.
When Bart and Lisa are disapproving of Homer's justification (at the tar pit) of trying to sell Stampy, they pose a stance which is identical to sonic and tails.
There are footprints on the walls and the ceiling in Simpson's kitchen.
Signs at the Republican meeting: "We want what's worst for everyone" and "We're just plain evil."
Signs at the Democratic Party meeting: "We hate life and ourselves" and "We can't govern!"
The scene of Homer using multiple cleaners in the basement, getting dizzy from the fumes, and hallucinating that the mascots on the bottles are attacking him is cut in U.S. syndication (but can be seen on the season five DVD).
The premise of a choice between prizes of either cash or an elephant is identical to another promotion in which the cash was refused, bringing an Asian Elephant to Alaska and establishing a zoo.
First appearance of Cletus Spuckler, though he wouldn't go by Cletus until the season seven episode "Home Sweet Home Diddly-Dum-Doodly" and his last name wouldn't be revealed until season 13's "Sweets and Sour Marge" (though in that episode, his last name was Del Roy, not Spuckler). In "Yokel Chords" he is referred as Cletus Del Roy Spuckler.
Homer's near death experience regarding his falling into the Springfield Tar Pit was later referenced in I Am Furious (Yellow), specifically when he, while expressing amusement at a tipsy Stegosaurus walking into a tar pit in the teaser clip for When Dinosaurs Get Drunk, mentioned that "[Homer's] been there, man."