Detective Da Fino, the PI hired to find Bunny Lebowski and played by Jon Polito, expresses his admiration of The Dude's apparent playing one side against the other throughout the movie. In Miller's Crossing, Jon Polito plays a mob boss who is victim to and absolutely hates a double-cross.
Walter's oft-repeated line "shut the fuck up Donny!" is precisely written because Buscemi's character wouldn't shut up in Fargo.
Which nearly became his type. Goodman said in an interview that a lot of the roles offer to him post-Lebowski were variations of the blustering Walter character.
Also, Steve Buscemi's role as a clueless, laid-back slacker who can't get a word in edgewise was written as a jokey inversion of the motor-mouthed psychopath types he'd played in Fargo and Reservoir Dogs. Walter's oft-repeated line "shut the fuck up Donny!" is precisely because Buscemi's wouldn't shut up in Fargo.
The Red Stapler: The White Russian has become somewhat legitimized as a "guy" drink thanks to this movie, as most people nowadays will just assume a man ordering one is a fan of The Dude.
The Coens originally wanted Marlon Brando for Jeffrey Lebowski. Names tossed around for the role included Robert Duvall (who passed because he wasn't fond of the script), Anthony Hopkins (who passed since he had no interest in playing an American), and Gene Hackman (who was taking a break at the time). A second "wish list" included an oddball "who's who," including Norman Mailer, George C. Scott, Jerry Falwell, Gore Vidal, Andy Griffith, William F. Buckley, and Ernest Borgnine.
In the original script, the Dude's car was a Chrysler Le Baron, as Jeff Dowd had once owned, but that car was not big enough to fit John Goodman so the Coens changed it to a Ford Torino.
In the original script, it was revealed that Walter was never actually a Vietnam veteran. Following Donny's funeral, the Dude was to yell at Walter, "You were never fucking in Vietnam, Walter".