In Raising Arizona (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.
In Barton Fink (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. 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).
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.
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.
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. In a way, this makes Norville the Hud sucker proxy.
The main theme music of the film is the uncredited Adagio of Spartacus and Phrygia from the ballet Spartacus by Aram Khachaturyan. This music was also used as the main theme for BBC TV's series The Onedin Line. The music played behind the black and white newsreel is Non-Stop by John Malcolm, used by Independent Television News in the UK in the 1950s and 1960s to introduce their main news bulletins. Malcolm apparently composed the piece to blow a raspberry at the musical prejudices of his tutor.
The secretary of the Hudsucker brainstormers (uncredited 'Mary Beth Peil') is reading throughout the Hulla Hoop manufacturing sequence the novels "War & Peace" and "Anna Karenina" by Leo Tolstoy. The idea is to show that the brainstormers are really taking their time to determine the name of the product since the novels have, respectively, 1,225 and 864 pages and are commonly known for being books you would spend a lot of time reading. In her case, if you'd consider 4 minutes per page, 8 hours a day, both books would've taken 18 days to read.
Sam Raimi:
in the Hulla Hoop manufacturing sequence as one of the Hudsucker brainstormers. We don't see his face, only his silhouette and we hear his voice.