Continuity mistake: At the end of the film the Monster tells Dr. Frankenstein, to leave. The Doctor and his fiancee run off. The Monster grabs a lever and says "We stay, we belong dead." He pulls the lever which blows up the castle. If you look to the left of the screen as the roof is collapsing, you can see Dr. Frankenstein knocked out on the stairs. Seconds later they cut to the Doctor and his fiancee running to safety outside the castle. It turns out in the original ending Universal killed the doc, but it tested poorly with audiences. They probably wanted a happy ending so they did a new ending where the doc lived, but they could not afford to blow up that castle again.
Suggested correction: We see Henry Frankenstein leaning against the wall with his arms outstretched, bracing for the collapse of the watch tower.
Continuity mistake: When The Monster is roaming in the woods early in the film, he comes across a shepherdess and her flock of lambs. Having fallen in the stream and been pulled out by The Monster, she starts screaming. In the long shots, The Monster puts his hands across her mouth very quickly to silence her, but in the close up shots of her, his hands are missing, even though they keep switching between the two shots.
Continuity mistake: After escaping the burning mill, the Monster is wandering through the forest when he comes upon a small pool of water. He placed his burned arm into the cool water, then leans further in order to take a refreshing drink. He sees his reflection in the water. The mirror image shows the scar on his forehead to be on the left side, when it should be on the right. The film was reversed by accident and not corrected.
Continuity mistake: When the hermit teaches the monster that fire isn't always bad, he has a cigar in his mouth. When he gets some firewood, the cigar is suddenly in his hand.