On the advice of Sam Raimi, the Coens went door-to-door showing potential investors a two minute 'trailer' of the film they planned to make. They ultimately raised $750,000 in a little over a year, enough to begin production of the movie.
The title is based on a phrase from the Dashiell Hammett novel 'Red Harvest', in which "blood simple" is a term coined to describe the addled, fearful mindset people are in after a prolonged immersion in violent situations. Blood Simple writers Joel Coen and Ethan Coen later made Miller's Crossing (1990) which is loosely based on that novel.
The finished film was brought to L.A. and shown to the major studios, and all passed on the movie. Later that year it was accepted into the 1984 New York Film Festival, and then shown at the Toronto Film Festival, where a deal was made with Circle Films to distribute the movie domestically.
While Ray is driving with Marty in the back seat, the DJ heard on the radio is John Lievsay. He says his replacement at 6:00 am will be Mike Miller. Skip Lievsay and Michael R. Miller were the sound editors on Blood Simple.
Holly Hunter: voice on Meurice's answering machine. Hunter had auditioned for the role of Abby, but turned it down because she was performing a play in New York at the same time. So she encouraged her roommate Frances McDormand to go and audition for the role.
Shannon Sedwick: the lower part of her legs are seen playing "the stripper." Sedwick founded the musical comedy troupe Esther's Follies, and has become a matriarch of Austin, Texas' theatre community. She is best known in recent years for her musical portrayal of Hillary Clinton.
The trivia items below may give away important plot points.
A teaser trailer for the film was shot long before the movie was in production. It featured Bruce Campbell (filling in for the role later played by Dan Hedaya) bloody and crawling down the road, just like the movie.
Joel Coen had trouble convincing M. Emmet Walsh to pick his hat up off the ground in the movie's climactic ending scene. Walsh had a laundry list of all the reasons his character would not do such a thing, each of which Coen tried and failed to debate. After minutes of arguing on set, Coen asked Walsh "Will you please just humor me?", to which Walsh replied "I'm humoring you by doing this whole fucking movie".
Despite all of the gunfire and various altercations throughout the film, there are never any police present at any time, unlike Joel Coen/Ethan Coen's later films (especially Fargo (1996)) in which the police play a large role in the plot.