Production Design
Third Person
Although this film may give you the sneaky impression that we're seeing everything from The Dude's point of view (probably because The Dude is such a chill and righteous guy), we're actually seeing everything from a third-person point of view, which is that of the mysterious cowboy who narrates the film.
All of this perspective shifting is important because the cowboy is supposed to be the audience stand-in: he's as clueless as we are about what's going on, and like us, he's just happy to be along for the ride. Take the first scene, where he's struggling to figure out what's so important about The Dude: "Sometimes there's a man … sometimes, there's … a man …" The viewer is also struggling to understand what's so important about The Dude, who at that point is just a guy in a bathrobe in a grocery store drinking from a carton of Half & Half he hasn't yet paid for.
Location, Location, Location
The Big Lebowski was filmed on location in and around Los Angeles, which is what gives it that authentic L.A. noir feel. All of the bowling sequences were filmed at a real bowling alley called Hollywood Star Lanes, which has since been closed down and turned into an elementary school. (There's a sequel here somewhere ...) The scene where Walter and The Dude meet for coffee was filmed at an actual coffee shop in Hollywood called Johnie's Coffee Shop. Well, "actual" no more: originally a fully operational coffee shop, Johnie's closed in 2000 and is now a historical landmark, probably because so many films have featured it, American History X (1998) and Reservoir Dogs (1992) among them.
Contemporary Classic
There are a lot of ways in which The Big Lebowski feels like a product of a different time. There's the '60s and '70s music, for one, and The Dude's laid-back hippie attitude for another. There's also the Busby Berkeley scene, which harkens back to the '40s, and the noir elements, which originated in crime novels from the '40s and '50s.
Another aspect of The Big Lebowski that makes it instant classic material is the fact that it has the old-school, hyper-authentic look of being shot on film. And that's probably because it was. Digital film had only just begun to see the light of day by the time The Big Lebowski was released. The Last Broadcast, the first film to be shot, edited, and distributed digitally, was released in 1998, just months after The Big Lebowski hit theaters.
Even if digital technology had been widely available during the making of The Big Lebowski, the Coen Brothers would have probably stuck with film over digital. Why? They were going for a Raymond Chandler '40s feel, and the Coens are nothing if not authentic. Digital is too crisp and clear for a fuzzy guy like The Dude.