Audio problem: When the monster is climbing up the laboratory steps following the music Frau Blucher is playing on the violin, she says, "Your grandfather would play this music for the creature he was making", her mouth does not move.
Continuity mistake: After Dr. Frankenstein dismisses the class, a black female student sitting in front of Herr Falkstein is already standing, readying to leave, but the next shot of her shows her just getting up from her chair.
Continuity mistake: After the monster has been given the sedative, Dr. Frankenstein collapses into a chair with Inga behind him and Igor by his right side. The next shot shows Igor gone and Inga running into the frame asking if the Doctor is all right.
Continuity mistake: When Frau Blucher announces that Victor was her boyfriend, she is alone in front of "the works" electrical panel, but the next shot shows the monster right next to her when he becomes frightened by the sparks thrown off by the electrical panel.
Continuity mistake: In the central nervous system lecture scene, Dr. Frankenstein's right hand is just over and above Mr. Hilltop's left shoulder, but the next shot shows the doctor about a foot away from Hilltop and his right hand level with Hilltop's left elbow.
Continuity mistake: When Dr. Frankenstein, Inga, and Igor meet Frau Blucher in the castle's main room, Igor is several feet behind Inga, but the next shot of the group shows him immediately behind her.
Continuity mistake: When Igor is holding onto the cemetery gate, his hands swap between angles from holding two bars close to each other, to having an empty bar in between.
Continuity mistake: Frederick Frankenstein only throws two darts through the window. But there are 9 darts in the car tires outside.
Revealing mistake: When Helga is sent flying into her room, the support cable that is attached to her is visible.
Audio problem: When Frederick is playing darts with Inspector Kemp, the last dart that Frederick holds flies backwards when he raises his arm quickly causing the dart to land on the floor, but when he throws his now empty hand forward, the sound of the window breaking is heard.
Continuity mistake: The monster puts his bowl way above the pot for the blind man to serve him. A frame later from a different angle, bowl and pot are at the same level.
Continuity mistake: When Dr. F arrives at the train station there's a lot of smoke/fog around him. In the close-up that comes a split second later it's all gone.
Continuity mistake: Dr. F arrives at the train station and stands to the left of the candle light. A second later he is right in front of it.
Continuity mistake: When Dr. F meets Igor and says "You were sent by Herr Falkstein, weren't you?", the expression on Igor's face from a side view doesn't match the immediate following the front shot (smiling / serious). The rest of the shots changing back to front do match.
Continuity mistake: At the cemetery gate, Dr. F tells Igor to crouch, which he does but very slightly. In the following angle Igor's position is totally different, being crouched at ground level with his hands on a different place.
Continuity mistake: When watching the grave diggers with Igor, Dr. F's hand on Igor's shoulder swaps sides depending on the angle.
Continuity mistake: When Dr. F climbs up the hay cart, the first wide shot shows him with his waist above the cart. The next shot, from the cart's POV, shows him only shoulder level.
Continuity mistake: When Frau Bluecher is talking to the Monster for the first time, she puts her hand on his head. In a closeup shot of the Monster's face her hand and arm are missing.
Audio problem: When they first find the monster conscious, Frederick says "Is the sedative ready?" The reply, "Yes, doctor," comes from Frau Blucher, who isn't there, and doesn't make another appearance in the film until she releases the monster and he escapes. It should've been either Inga or Igor saying it.
Continuity mistake: When the blind man serves soup, there's a spoon in a cube on the left skewed to the right. A couple seconds later it's straight.
Answer: It's called "Transylvanian Lullaby" (as they tell you in the film) and was composed for the movie.
Myridon