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.
Enforced Method Acting: During the dream sequence when the Dude is looking up at a series of dancing girls, the expression he wears on his face is the result of the extras (with the encouragement of Jeff Bridges' wife and daughter) having stuffed their briefs with hair to make it seem as though they had ungroomed nether regions.
Fake Nationality: The German nihilists played by Peter Stormare (Swedish), Flea (Australian), and Aimee Mann (American). The fourth nihilist was played by an actual German, Torsten Voges.
Parody Religion: The film has spawned its own, The Church of the Latter-Day Dude, or Dudeism.
To some degree, John Goodman as Walter Sobchak. His characters, when not directed by the Coen Brothers, tend to be nice, huggable, jolly guys. Walter is anything but. 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.
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".
For the pinball:
Troubled Production: Quite a turbulent one. Universal Studios contributed plenty of Executive Meddling during development and threatened Dutch Pinball with pulling the license after premature showing of a prototype with unapproved artwork. Dutch Pinball's Director of Marketing and Communications, Phillip Weinberg, resigned due to said problems and made several revealing and accusatory statements about the company. And just when everything appeared fine, it came to light in 2017 that Dutch's Pinball's contract manufacturer, ARA, was halting production of The Big Lebowski upon claims that Dutch Pinball had not paid them sufficiently. They also were holding completed machines hostage from customers out of protest. Dutch Pinball severed ties with ARA and announced that they found a new manufacturer, though nonetheless have been derided by those still awaiting their games.