The police chief in Malibu (combined with Nausea Fuel, because he makes you so sick) throwing the coffee mug right in Dude's face after he replies "Sorry, I wasn't listening" to his long and cautionary "The Reason You Suck" Speech (in a way, the irritant indeference makes it look even funnier while almost justified, nevertheless). Enhanced by Dude's reaction ("Ow, fucking fascist!").
As The Dude is being hustled into Mr. Lebowski's limo, he yells out, "Hey, careful, man, there's a beverage here, man!"
"Also, Dude, Chinaman is not the preferred nomenclature. Asian-American, please."
The thug who defaces the rug pronouncing "Ever thus to deadbeats" in the process, as if making a political point a la "Syc Semper Tyrannis" in the assasinations of Gaius Julius Caesar and Abraham Lincoln.
The Dude trying to pull a Royal "We" with Big Lebowski when he realizes he inadvertedly mentioned Walter came along.
The Dude thinking the boys in the picture are Big Lebowksi's literal children from different mothers,
Racially he's pretty cool huh?
Many of the gratuitous echoes and words one character borrows from another, "parlance of our times", unchecked aggression which will not stand, coitus, johnson etc...