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.
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.
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.