Visible crew/equipment: In the final scene where Frankenstein is fighting the Spacemonster on the spaceship, there are upshots of the monster attacking to make him look larger, but looking right behind his head you can see a ceiling mounted fluorescent light and electrical conduit; neither of which would have been on a spaceship.
Revealing mistake: During practically every scene with Dr. Nadir, the prosthetics to make his cranium look more 'alien' are visible. In particular, when the Queen realises he's been shooting down spaceships and not missiles and calls him a 'fool', at the back of the neck the line where the concealing make-up ends is evident. Throughout the rest of the movie the other Martians have similar if not even more obvious bald caps. (00:17:45)