Character mistake: When they exit the bowling alley with the dog, the dog is never put in the car, only the cage.
Visible crew/equipment: As The Dude enters his apartment, having left Ralphs, a stage hand can be seen in a window of another apartment. The stage hand ducks quickly.
Continuity mistake: When the Dude shows up at Maude's place (the time where the video artist is laughing annoyingly), pay attention to Maude's bangs changing positions between several shots. Sometimes the hair is raised up on the left side of her forehead and other times the bangs are straight across. It's most noticeable after she pours a drink and turns around.
Continuity mistake: In her studio, Maude dumps a bunch of trinkets on the counter. While she is on the phone, some of the items disappear and then reappear.
Factual error: This film takes place in the early 90's. When Walter and the Dude are talking about the toe in the cafe, you can see late model cars driving by on the street, such as a late model Ford Explorer and a Cadilac. This is also evident when the Dude gets kicked out of the cab and a mid '90s Nissan Maxima drives by.
Continuity mistake: When the Dude joins Mr. Lebowski in the West Wing, where he was in seclusion, he is handed Bunny's ransom note by Brandt. As he reads the note he smokes a joint. Through the entire reading sequence he moves the joint from his mouth to his hand and back. Watch how several times the joint is in his hand, while you see a shot of the note and the Dude's hands, but when the shot changes to overall view, the joint is suddenly back in his mouth and he retrieves it again.
Other mistake: Near the beginning of the movie, the Dude is shopping at Ralph's. He is writing a check, and dates it September 11th, 1991. At the same time he looks up to see a TV with President Bush saying "This aggression (against Kuwait) will not stand." The incident against Kuwait started in the summer/fall of 1990, not 1991. The Stranger (Sam Elliot) and Walter also mention the Gulf War in the present tense.
Continuity mistake: When The Dude is sitting in the chair talking to Mr. Lebowski, his jacket is open so that the hole in his shirt shows, then closed, then more open again from shot to shot.
Other mistake: As "Brother Seamus" slams the door of his Volkswagen shut before "fighting" The Dude, the volume of the radio drops, although he had the window rolled down and did not have time to roll it up before getting out of the car.
Revealing mistake: In the scene near the beginning it shows a big guy converting a 7-10 split and celebrating. If you watch it closely you will realise that the 7 pin is lined up too far to the left and the ball is already in the gutter when it hits the pin. The movie makers could have at least bothered to repaint the pin placement lane markings so it would not be so obvious that the pin had been moved.
Continuity mistake: In the porno film that Maude shows to the Dude, Karl is seen driving a BMW 318i convertible in the E36 generation. This particular model didn't come out until 1994.
Continuity mistake: When the Eagles-loving cabbie goes to throw the Dude out of his cab, a black Nissan Maxima passes by the cab. This particular model didn't come out until 1995.
Continuity mistake: When the Dude is in Maude's limo, his glass of White Russian is half full. The angle cuts to the driver when he says "Fuggetaboutit." When we cut back to the Dude, his glass is almost completely full.
Continuity mistake: In the scene in the limo, with the Dude drinking his white Russian, some shots show him with a milk moustache, then the shot changes, and then when it returns he doesn't have a moustache. The next time the camera left the dude and returned, he has the moustache back.
Continuity mistake: When Dude is talking to the stranger at the bar the straw in his glass changes sides of the glass very often, but Dude isn't drinking in this scene.
Continuity mistake: When Donny bowls the last time, the time when he only hits nine, just as he bowls a man with a blue bag walks behind him, then it cuts to the skittles and then back to him, and the man keeps walking from where we last saw him as if he paused for the few seconds while the skittles were showing.
Visible crew/equipment: Towards the end, when the Dude starts getting angry after Walter accidentally scattered the ashes all over him, you can see a black wire under the Dude's shirt going into his pants, most surely a microphone.
Continuity mistake: In the bowling alley, when Walter says "Am I wrong, am I wrong", there is a shoe on his left, then camera switches to the Dude, and when it comes back to Walter the shoe disappears.
Character mistake: When Walter brings Cynthia's dog in the carrier to the bowling alley he refers to it as a Pomeranian while it is actually a terrier. Somewhat related, when the the Nihilists confront Dude in the bathtub, the dude refers to the ferret as a marmot. Walter later refers to the ferret as an amphibious rodent. Perhaps he was thinking of a mink.
Suggested correction: These were purposeful taxonomic (funny!) jokes.
Audio problem: When the Malibu Police Chief throws his coffee mug at The Dude you hear it glance off his forehead but never hear it hit the floor. Even if it somehow didn't break, it's a solid floor (not carpeted) so the impact would've made a noise.
