Continuity: The close-up of Frankenstein's monster burning in the flames at the end is very obviously not 'Glenn Strange'. In fact, it is a shot of Lon Chaney Jr., borrowed from the earlier Ghost of Frankenstein.
Crew or equipment visible: When the vampire bat is flying, the strings guiding it are visible.
Factual errors: In the opening scene, and at various moments during the film, Count Dracula casts a visible shadow: Classic cinematic vampires cast no shadows.
Miscellaneous: Although the Frankenstein Monster has been mouldering in a warm, moist environment for years (in the muddy caves at the base of the cliff), his clothing is apparently immortal, too, for in the very next scene after his discovery in the caves his clothing appears pristine and brand new, showing no signs of the inevitable mold and rot that ordinary fabric would incur in such conditions (unless, of course, the Doctor has re-dressed him in identical clothes, which seems unlikely). In contrast, the clothing of Dr. Niemann, who was buried/and found with the Monster, has completely rotted away, to reveal only bones.