Interrogation by Vandalism: This is the reason The Dude's rug gets pissed on at the beginning of the movie.
Also, the "You see what happens, Larry!?" scene.
I Resemble That Remark!:
Stranger: Do you have to use so many cuss words?
Dude: What the fuck are you talking about?
Ironic Echo: The Dude, having turned the tables on The Big Lebowski: "Where's the fucking money, Lebowski?"
Irony: The film has a lot of it.
For a stoner who supposedly "abides" and puts on airs of being calm, the Dude gets angry a lot and often tries to change, or unintentionally winds up changing, events around him that he wants no part of.
As it turns out, the Big Lebowski doesn't actually have any money of his own, despite his posturing and elitist bluster at the Dude for fitting into his bias of the lazy, unemployed leeches looking for a handout.
In one scene, Walter, the (as he'll tell you) Vietnam veteran who pulled out a pistol on a fellow bowler over tournament rules and constantly argues with people over his right to be angry, wimps out and flashes the peace sign to an angry owner of the car he just angrily wrecked. Earlier, he correctly points out he is, in fact, calmer than The Dude is.
Maude, as an artsy, Avante-garde type who dislikes capitalism (as most artists do) and materialism, gets involved to protect her family's money… and her mom's rug.
The Nihilists, who "care about nuzzink!" and think they're uncaring villains defying weak men's' laws, whine that it's not fair when it's revealed neither the Big Lebowski nor the Dude have the money they wanted.
I Take Offense to That Last One!:
Dude: Fuck the Tournament. Fuck you, Walter.
Walter: Fuck the Tournament?
Incest Subtext: Even though we're assured that Jeffrey "The Dude" Lebowski (the hippy bachelor) and Jeffrey Lebowski (the paraplegic billionaire philanthropist) have no relationship to each other, it's more than a little bit disturbing when the Dude winds up impregnating Maude Lebowski by the end of the movie, thus assuring us that Maude's child will still carry the Dude's name.
It's All About Me: Walter, who makes everything about how he fought in Vietnam just to see what the world has become.
Waitress: Sir, if you don't calm down, I'm going to have to ask you to leave.
Walter: LADY, I GOT BUDDIES WHO DIED FACE DOWN IN THE MUCK SO YOU AND I COULD ENJOY THIS FAMILY RESTAURANT!
It Began with a Twist of Fate: The entire plot of the movie gets kickstarted because a pair of Stupid Crooks went to the wrong Jeffrey Lebowski's house to try to collect on his wife's debt.