Factual error: It appeared that, during the engagement with the Serapis, every hit by either ship's guns resulted in an explosion and fire. Unfortunately, explosive shells wouldn't be used on shipboard (aside from bomb vessels) until the next century.
Continuity mistake: When Bugs is performing his shooting stunt in the saloon, you can see the entrance behind Sam has nothing between it. When Sam tells Bugs he's missed, we cut to Bugs who says "Wait!" and then return to Sam, and this time there are doors between the entrance.
Deliberate mistake: For all exterior shots on the surface of Mars, the crew's "pressurized" space helmets have no face-plates (their faces are fully exposed to the hostile Martian environment). The transparent face-plates they intended to use reflected far too much studio set lighting, such that the glare would have obscured the actors' faces. On a $200,000 budget and a 10-day production deadline, they simply scrapped the face-plates and shot the scenes with wide-open helmets.
Continuity mistake: When Sylvester is looking through the window with his binoculars, he looks at Spike and you can see there is a bowl with a bone next to his kennel. But when Sylvester sneaks past Spike's kennel after entering the yard, the bowl has gone.
Revealing mistake: Near the beginning, when police Lieutenant Rowan is inquiring on the death of Ken Drake, there are only 4 men in the room, all facing one another in a wide shot. The camera cuts to a close-up of Dr. Bradford for a couple of seconds, and there is a distinct puff of cigarette smoke passing behind him, but none of the characters in this scene are smoking. Lieutenant Rowan does smoke later in the film (in fact, he's the only character who smokes), but he's not smoking in this early scene. Apparently, the close-up of Dr. Bradford was borrowed from omitted footage in which Lieutenant Rowan was smoking.
Factual error: Karnak was an Egyptian city, not one of their gods.
Continuity mistake: When Bugs hits the tree after arriving in the Ozarks, some earth from the tunnel burrow he has made falls onto the ground. But when he emerges from the ground, the earth disappears.
Continuity mistake: The car is out of gas, and Sylva Koscina gets impatient. As the shot changes, Walter Chiari's arm is on top of the car door (it wasn't in the first shot) and Dorian Gray crosses again her arms on top of the bag - assuming the same pose she already had. (00:17:00)
Continuity mistake: When Witch Hazel is chasing Bugs Bunny up the castle tower, Bugs throws a stone through the window before Hazel appears from behind the curtains. When we see Bugs dressed up as Romeo, the glass panes have disappeared, and when we see Hazel dressed up as Juliet, they are back again.
Continuity mistake: Christopher Lee looks outside his useless nephew's room and spots two hot Swedish girls. Renato Rascel has a bottle of wine in hand and walks towards him, but the bottle is gone when he tries to stop him. (00:23:40)