When Frankenstein introduces his new assistant to his lab and shows him the brain, eyes, and arm, he states that the brain is responsible for moving the hand away from a flame; in actuality, the withdrawal reflex involves only the spinal cord and does not involve the brain.
After Dr. Stein removes the brain from the victim on the operating table and slips it into a glass container with a clear liquid, the "blood" turns into droplet form much like oil and sinks to the bottom rather than dissipate like actual blood would.
When Frankenstein's dwarf assistant Karl looks at his new body in the glass case in Frankenstein's lab, the hand of the body is moving.
Peter Cushing's face being shown was not a goof. It was the face of the body he had made to resemble his own face that later had his brain transplanted to. It's ironic that the only successful monster was in fact Dr. Frankenstein himself.
When Gerda leaves her boyfriend she is attacked by Karl after she descends a flight of steps. Half way down the steps is a bright yellow, 20th century, metal mesh litter bin attached to the wall.
Frankenstein calls his patient at the end "Wendy". "Wendy" as a girl's name was not used until J. M. Barrie used it in "Peter Pan" in 1904, well after the action of the film.
In the Baron's "dining room," running water, and sink with drain, did not exist in 1860/65. He would have had to use an outside well/ pump. Neither did electricity, with lights (to power his brain/eyes/hand experiment), until 1885.
Of course, like in other Hammer Frankenstein or Dracula films, action takes place in a city that don't exists in reality. You won't find a German city called "Carlsbrück". But it sounds familiar to Germans anyway.
Peter Cushing's face appears during a very short sequence instead of Oscar Quitack's. This has been confirmed by Cushing himself and may be some kind of private joke.