Joel Coen remarked that "the film doesn't really have a plot. That concerned us at one point; that's why we threw the cat in."
In an interview included on the DVD, Ethan Coen said, "The cat was a nightmare. The trainer warned us and she was right. She said, uh, "Dogs like to please you. The cat only likes to please itself." A cat basically is impossible to train. We have a lot of footage of cats doing things we don't want them to do, if anyone's interested; I don't know if there's a market for that."
The Bud Grossman character played by F. Murray Abraham is based on Albert Grossman, who ran the Gate of Horn club in Chicago and managed acts like Bob Dylan, Peter Paul & Mary, and Janis Joplin.
Although there was talk of nominating "Please, Mr. Kennedy" for a Best Original Song Oscar, the fact that it was an amalgam of several period songs, novelty and otherwise, meant the Academy had to pass.
This is the second Coen Brothers movie with a plot partly inspired by Homer's The Odyssey. When the first one, O Brother! (2000), came out, the Coen brothers told several interviewers that had never actually read The Odyssey; in 2013, they told Terry Gross that they had still never gotten around to reading it. One of them said to Gross, "Yeah. It's right by my bedside table. I keep looking over at it and going, ugh."
Joel Coen, Ethan Coen: [Kubrick] The first few shots of the scene in the bathroom were filmed as an one-point perspective, the same way Kubrick filmed the memorable meeting between Jack Torrance and Grady in El resplandor (1980) also taking place in a bathroom.
Ethan Coen, Joel Coen: [sound effects] 'Thump thump' sound of car tires running over the seams in the highway when Llewyn is traveling to Chicago. In Fargo (1996), you can clearly hear the exact same sound effect as the character of Grimsrud drives the Cutlass Ciera in pursuit of the couple who witnessed the state trooper murder.