One of the inspirations for the character of Walter is the Coen Brothers' friend, writer-director John Milius, an infamously bombastic right-winger with an obsession with all things militaristic and an enthusiasm for guns. His girth, beard, hair style, and shades are also all reflected in Walter's physical appearance. The Coens had tried to cast Milius in the film Barton Fink (1991) in the part eventually played by Michael Lerner.
At the end of the movie, when the Dude and Walter discover Bunny's crashed car; the car's brake lights are illuminated (it's not due to her headlights because her third brake light is on), despite the car being empty (so there is no one to hold the brake pedal down).
After the introduction of "Jesus" there is a shot from left to right, ending with Walter Sobchak. You can see a reflection of the cameraman in his left eyeglass.
The following FAQ entries may contain spoilers. Only the biggest ones (if any) will be covered with spoiler tags. Spoiler tags have been used sparingly in order to make the page more readable.
Q
What's that song that is heard throughout the movie?
A
"The Man in Me" by Bob Dylan plays at the opening credits and again when The Dude dreams about bowling after being knocked out. "Tumbling Tumbleweeds" by Roy Rogers & Sons of the Pioneers serves as The Stranger's theme. It plays during the introductory monologue and again when the Stranger appears next to The Dude and orders a sarsaparilla. For the rest of songs and their corresponding scenes in the movie try here.
Q
To whom was the line "Life does not stop and start at your convenience..." directed?
A
According to rumor, the line "Life does not stop and start at your convenience, you miserable piece of shit" was directed at Joel Coen, when John Goodman thought he said "cut." Source here. However, this reason is obviously a joke propagated by the Coens. The line is in the original shooting script and clearly fits the tone of the scene. Walter is expressing his sentiments about the Big Lebowski thinking he can summon the Dude during league-play. It may even be directed at Donny, since he is (again) attempting to enter the conversation without prior knowledge of what the Dude and Walter are talking about.