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.]
Deliberate 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.