Continuity mistake: When Drebin first meets Ludwig, you see the shelf of vases. To the left of that is the fancy painting. However, when Drebin accidentally sets fire to the office, he rushes to the shelf to catch the vases as they fall. He then look to his right to see the flames getting close to the painting. He moves to his right (pulling down the shelf of vases in the process), takes the painting off the wall, and impales it on the plant. It should've been the other way around. Drebin should've looked and moved to his left instead of his right.
Continuity mistake: After deactivating the hypnosis, Ludwig has the remote in his left hand. A second later, it's in his right hand.
Continuity mistake: Just before Frank accidentally nudges one of the fishermen into the river with his car, if you look in the background there is a police car. In the next shot of Frank getting out of his car on the pier, the police car is now noticeably much closer than in the previous shot.