Continuity mistake: When The Dude enters Lebowski's office the telephone is on the far right of the desk and the lamp is on the far left with 3 wooden objects between them. During the shots of The Dude, when he is talking, the phone and lamp are much closer together and the wooden objects aren't there.
Deliberate mistake: When we are introduced to Jesus, during his slow motion roll, the camera cuts to the ball hitting the pins and then back to Jesus doing a celebratory dance. For some un-known reason, the film of the ball hitting a strike is actually back to front (see the posters above the lane are in mirror image to what they should be). Given that a bowling lane is perfectly symmetrical, if anyone's got an explanation, I'd love to hear it... [Jesus bowls with his right hand. If the scene was played the correct way, you would realize the shot of the ball rolling was done by a LEFT HANDED bowler...so obviously rather than re-shoot the scene with a right-handed bowler they reversed the shot. Voila. Still a mistake but there's why.]
Continuity mistake: When the Dude's driving home from the doctor's, he passes a yellow truck, visible through the side window, when he throws his joint against the door window. If you compare the shot where he grabs for his joint and the next one where he sprinkles the beer, you'll see he passes the truck twice.
Continuity mistake: The Dude's driver's-side door is unusable after his car is stolen and retrieved, and we see him using the passenger door at least once after he takes the car home. But then at Larry Sellers' house, which they visit pretty soon, The Dude gets out of the driver's door as if nothing had happened; I doubt he'd have bothered to have it fixed in that short time.
Visible crew/equipment: When the Nihilists are ordering food at the restaurant, you can see the reflection of the camera and cameraman in the window behind them. Watch as the scene pans around and you can see the camera and the cameraman move as well. Could the person behind the camera be Roger Deakins?
Continuity mistake: When the Dude is in Jackie Treehorn's estate, he pencils over a pad of paper to see what Jackie wrote down while he was on the phone. He then hurriedly crumples up the piece of paper and shoves it in his wallet. Then, when we see the Chief of Police of Malibu looking through the contents of The Dude's wallet, the paper is there, neatly folded in fourths.
Continuity mistake: The Dude is driving, being followed by Da Fino. Suddenly he realises the tail has disappeared and hurriedly pulls the car over. As he looks out his driver's side window, we can see he's wearing his sunglasses, but when he checks the other window, his sunnies are gone.
Continuity mistake: There's one scene where The Dude is taking a bath, and three Germans threaten him with a marmot (actually a ferret). When they take the little animal out of the water, you see Dude's head and in the back four candles: yellow, blue, red and white. The yellow and red one aren't burning; the blue and white are. The next shot of the Dude's head you see that the yellow, blue and red candles are burning, the white one isn't.