The shot in which the camera moves in on the mother discovering that Nathan Jr. is gone is a direct homage to The Evil Dead (1981), a film on which Joel Coen was an editor.
The alarm button the clerk presses in the convenience store reads "Odegaard-Trend Security." This is the name of the security company in Sam Raimi's Crimewave (1985).
The character Leonard Smalls is a reference to Lenny Small from "Of Mice and Men."
H.I. can be seen wearing a uniform with the name "Hudsucker Industries" written on it. This is also the name of the company in The Hudsucker Proxy (1994) also by the Coen brothers.
When Nathan Arizona is being interviewed one of the microphones has "KOIN" written on it. This is a reference to the filmmakers, the Coen brothers.
Although the letters POE and OPE are shown reflected in the mirror in reverse, the writing on the "We aim to please..." sign on the same wall is not reversed. Later, when the Biker breaks down the door, you can see that the sign is actually printed in reverse lettering.
Florence, Arizona is the site of a State Prison...and also the name of the mother of the quints in the movie.
When the Biker played by Randall 'Tex' Cobb enters the rest stop bathroom, he notices pomade and sniffs it. This was the pomade Gale used in an earlier scene. Gale (John Goodman) is tracked down by the Biker because of the pomade smell. In O Brother, Where Art Thou? (2000), a later Coen Brothers' movie, Big Dan T (Goodman again), during the lynching scene, sniffs out Everett's (George Clooney) Dapper Dan pomade. Everett is also tracked by the posse throughout the movie because of the scent of the pomade.
Fifteen babies played the Arizona quintuplets in the film. One of the babies was fired during production when he learned to walk.
The shot where Evelle and Gale stop just before hitting the car seat with the baby in it, was filmed in reverse, with the car driving away from the seat.
Randall 'Tex' Cobb was not familiar with riding motorcycles prior to filming. While shooting the scene where he rides up to inspect the hole where Evelle and Gale had escaped from prison, he actually crashed into the hole on one of the takes.
H.I. McDunnough's first name is revealed to be Herbert.
The $30,000 that Leonard Smalls talks about as "1954 dollars" would be equal to just over $120,000 in 1987.
When the cops chase H.I. through a house, Nathan Arizona's Unpainted Arizona commercial seen earlier in the film is playing on TV.
The line, "Life is hard on the little things," used repeatedly in the film was originally spoken by Lillian Gish in The Night of the Hunter (1955) as she protects her children. In the accompanying scene an owl takes a young rabbit.
The Coen brothers wrote Holly Hunter's character specifically for her.
The lullaby that Ed sings to Nathan, Jr. is the song "Down in the Willow Garden", a folk song about a man sentenced to death after brutally murdering his fiancee.
Nathan, Jr. doesn't cry at all throughout the entire movie. But all the other main characters do at some point.
During the chase scene through the grocery store, the movie's theme can be heard playing on the store's music system.
While many reviews refer to Tex Cobb's character, Leonard Smalls, as a "Harley riding biker," the motorcycle in the movie is in fact a Honda Shadow that has been subjected to the "Rat Bike" treatment along with some extra flame-emitting plumbing. The Shadow is slightly smaller than a Harley Big Twin, which would give Cobb's character a bit more stature than he already has. One must also assume that since the bike is trashed near the end of the movie, it saves the production company a few coin.