George Clooney has stated he learns a lot from the Coen brothers for his career as a director and tries to have things running the same way they do on his films, even hiring their storyboard artist, J. Todd Anderson, on two of them.
According to costume designer Mary Zophres, even cheap suits look good on Brad Pitt. Thus, for the scene where his character Chad wears a cheap suit, she had to tailor a suit with a purposefully bad and ill-fitting cut and a horrid-looking wool tie.
When Linda and Harry go to the theater to watch "Coming Up Daisy", the board displaying showtimes lists "Hail Caeser" as being one of the films showing at the theater. This is a reference to Hail, Caesar!, the 2016 Coen Brother's film of the same name, which would not be produced for eight more years.
The Coen Brothers wrote the character Osborne Cox with John Malkovich in mind. Brad Pitt's character was also written with the actor in mind, inspired by a commercial for which he suffered a similar haircut and dye job. Indeed, the Coen Brothers noted at a Q&A session at the Venice Film Festival that all the leading characters were written for all the leading actors, with the exception of Tilda Swinton.
The poster for the film within the film, "Coming Up Daisy", states it is based on a book by Cormac McCarthy (who really wrote the book "No Country For Old Men", which the Coens' previous film was based on), and that it was directed by Sam Raimi (a friend and collaborator of the Coens').
On the Criterion Blu-ray of Blood Simple. (1984), in "Shooting Blood Simple" featurette with Barry Sonnenfeld, Joel Coen and Ethan Coen reveal that the joke involving the sex chair built by Harry Pfarrer was taken directly from key grip Tom Prophet Jr., who built a very similar device in real life, and cited the exact same reasons as Harry.
When Harry's wife is on the Seattle show, the show's host interrupts her, saying that "Dermot Mulrooney" is coming on after the commercial break. Dermot Mulroney is the actor that plays "Star of 'Coming Up Daisy'" in the actual film.
In Palmer's office there are some pictures on the wall behind Palmer on the right side. One of the pictures is a photo of Chilean dictator Augusto Pinochet shaking hands with Henry Kissinger, US Secretary of State. Kissinger and The CIA acknowledged having played a key role in the coup led by General Pinochet that toppled the Marxist government of Salvador Allende in 1973, the democratically elected president of Chile at the time.
The Coen Brothers and their long-time composer, Carter Burwell, decided that the movie should have a bombastic music score that suggested 'meaning without meaning' and chose Jerry Goldsmith's percussive music for Seven Days in May (1964), as its chief inspiration.
JK Simmon's character (CIA Superior) states that the US and Venezuela do not have an extradition treaty. In fact, there is an extradition treaty dating back to 1922, but the governments seldom cooperate.
When Harry goes to stay at Katie Cox's house after she breaks up with Osbourne, he brings along a purple "ramp", a sex tool from the Liberator line. After they collide he leaves the house only taking the "ramp" away.