In Raising Arizona (1987) (also directed by Joel Coen), factory workers could be seen wearing a uniform bearing the name "Hudsucker Industries". The Chief also says "Yeah, and if a frog had wings, it wouldn't bump it's ass a-hoppin", just as Nathan Arizona Sr did.
The song Waring Hudsucker sings as an angel is the same song Gale and Evelle sing after they've kidnapped Nathan Jr. in Raising Arizona (1987).
In Barton Fink (1991) (also by the Coens) John Goodman played a character who used the alias "Karl Mundt". In this film, John Goodman appears in a cameo as the announcer during the newsreel, and is credited as "Karl Mundt".
Norville describes Smitty (Bruce Campbell) as a "smooth-talking heel," which is actually a description of the character that Campbell played in Crimewave (1985). Also, several scenes in Crimewave are set in "Hudsucker Penitentiary". Both films were co-written by the Coen Brothers and Sam Raimi in the same summer (though 'Hudsucker Proxy' took almost ten years to get made).
"Hudsucker Proxy" was one of the incantations in the Book of the Dead in an early draft of Evil Dead II (1987).
The published script is introduced with a fake interview with "producer" Joel Silver (who is uncredited in the film). In this interview Silver claims that the Coens were difficult to work with and among other things wanted Ethan to play Tim Robbins's part and Jeanne Moreau to play Jennifer Jason Leigh's (despite of the age difference of 30+ years).
A sign on the wall in the Manhattan Argus pressroom reading "It must be fit to print. It must be accurate. Is it interesting?" is a close adaptation of one painted onto the wall of the pressroom in The Finger Points (1931).
Both products made by Norville Barnes (the Hula-Hoop, and the Frisbee) are products of the Wham-o company.
The death of Waring Hudsucker was inspired by a real-life incident. On February 3, 1975, Eli Black, the CEO of the United Fruit Company, smashed an office window with his briefcase and jumped to his death from the 44th floor of the Pan Am Building in New York City.
Dr. Hugo Bronfenbrenner, the psychiatrist who evaluated Norville for the board, was likely named after famous developmental psychologist Urie Bronfenbrenner.
Although not released on the film's soundtrack, the familiar, quick-tempo song heard when the children are making a mad dash to the toy store to buy the Hula-Hoops is called "Sabre Dance". It was written by Aram Khachaturian and is featured in his ballet, "Gayane". The song is often associated with juggling acts and such.
Norville is a "sucker" selected to be the puppet president, by Paul Newman who gained fame for playing the title role in Hud (1963). In a way, this makes Norville the Hud sucker proxy.