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.
Continuity mistake: When The Dude crashes the car into the pole, you cannot see Walter lying in the road. (00:36:18)
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.
Continuity mistake: When the Dude first meets Bunny by the pool, her lounge chair is in the bright sunlight, directly facing the sun. When he walks away, her chair is in the shade and the shadows show the sun is now to the side.
Continuity mistake: The Dude is holding a beer bottle when Walter yells "over the line" at Smokey, after Smokey says "huh?" the movie cuts back to Walter and the Dude, but the Dude is no longer holding the beer bottle. (00:17:00)
Continuity mistake: In the opening scene when The Dude's head is repeatedly shoved in the toilet, almost all of the water is pushed out of the bowl and it's nearly empty. Soon the bowl is once again full, even though the toilet had not been flushed, which is the only way the bowl is normally refilled.
Answer: Themmen plays a background bowler in pretty much all of the bowling scenes. I don't know if this is necessarily worth a credit, but I guess his agent disagrees with me.