Two of the names on the Krusty the Clown birthday list are the names of people who would later become part of the Simpsons staff: Ken Keeler and Patric Verrone (though Patric Verrone only wrote one episode of The Simpsons—season 17's "Milhouse of Sand and Fog"—and quit writing for The Simpsons in favor of working on Futurama)
Originally, after Homer panics over Bart's phony alien invasion message, he is seen mixing a punch bowl filled with Kool-Aid and rat poison in the kitchen. The censors objected to the suicide reference (and thought that more impressionable viewers would be drawn to imitating what Homer did), so the writers changed it to Homer getting a shotgun and running out to defeat the aliens (only to realize that it's Bart).
The three things Bart mentions he won't be able to do now that he's stuck in the well is smoke a cigarette, use a fake ID (which he would do in season seven's "Bart on the Road"), and shave a swear word in my hair (which is what Milhouse did during the Squishee bender on "Boy Scoutz 'n the Hood").
The media circus and carnival that results after news breaks about Timmy being trapped in the well mirrors that of the 1951 movie Ace in the Hole. The movie in turn was based on the real incident and media circus that resulted when cave explorer Floyd Collins was trapped and died in a cave in Kentucky in 1925.
In the late 1980s, Sony had a children's electronics product line called "My First Sony". Bart's microphone and amplifier strongly resembles one of the products.
Upon hearing Bart cry about being trapped in the well, Homer decides to dig Bart out himself, declaring "That's all I can stands, and I can't stands no more!" echoing a catchphrase from the TV series Popeye the Sailor.
The TV dance show "Soul Mass Transit System" is a parody of the television program Soul Train.
Homer serenades Marge by singing "Convoy". Originally the song "The Wreck of the Edmund Fitzgerald" by Gordon Lightfoot was to be used. However, Lightfoot told the Simpsons producers that he did not own the rights to the song, as he divided all royalties with the surviving families of the 29 men who perished aboard the SS Edmund Fitzgerald. Any use of the song would require permission from all of the surviving families. Rather than go along with that, the writers picked "Convoy" instead. "Convoy" would later be used on the Simpsons episode "Maximum Homerdrive" and the Futurama episode "Parasites Lost."