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.
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.