Deliberate mistake: After trying to get away from the monster, Costello finally unties the boat as Abbott rows away from the burning dock. The next shot of the boat has Abbott slowly rowing the boat, but you can see it's not moving as there's no wake, and when they jump off the boat after the Invisible man speaks, it doesn't rock, meaning the boat was mounted to something to prevent any movement, so they could make the jumps into the water.
Continuity mistake: If you look carefully at the monster (Frankenstein) you will see that his face is different in the ending scenes. The reason is, during the movie you see the monster take the woman doctor and throw her out the laboratory window. You then see the monster kind of stumble, which he really did and broke his ankle. So in the final scenes they replaced Lon Chaney Jr. as wolfman with a stuntman, and Lon Chaney Jr. finished the movie as the monster.
Visible crew/equipment: During the scene when Lou Costello is reading the narrative on Count Dracula we see the coffin door open and the candle on top of the box starts to descend. By the angle of the coffin door the candle would have easily fallen to the ground. If you look carefully you can see a thin black cord attached to the candle.
Factual error: In no place on Earth does the full moon occur five times in a row, as it is in the movie.
Continuity mistake: In a shot early in the movie, Costello is retrieving a bag for a customer. When he pulls the bag from the middle of the cart, it falls below other bags and packages. But when the shot changes and Abbott asks which bag is the customer's, Costello points to a bag on top of all the others.
Other mistake: When Abbott and Costello are bringing the first crate (Dracula) into the house of horrors, Abbott tells Costello twice to help with moving the crate. The first time Abbott says to help pull the crate, which is correct. The second time, Abbott says to help push, even though Costello is still pulling.
Other mistake: During opening scene, two faces of Big Ben show different times. One face shows 8:00 and the other shows 9:00.