Continuity mistake: When Inga, Frederick, and Igor reach the secret library, Frederick reaches for the door knob to grasp it with his right hand, but the view from inside the room showing them entering has Frederick's right hand opening the door without using the knob.
Continuity mistake: When the casket slides off the wagon, breaks open and cracks a couple of its wood slats, the arm from the body is not protruding from it until Igor and Frederick come up to it in the next shot.
Continuity mistake: When Dr. Frankenstein introduces himself to the monster with a soothing "Hello, there", his right hand is on the restraint over the monster's chest. The next shot shows the doctor placing his hand on the restraint again.
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: 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: 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: In the scene where Inga, Fredrick and Igor throw the net over the monster, Inga sticks the syringe of the sedative in the monster's back but does not push down on the top, yet the monster still falls over. A few seconds later when she collapses on the monster, you can see all of the fluid inside spray out. (01:12:05)
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.
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: The brain that Frankenstein draws on the blackboard in the first scene is different from the one behind him as he is seated and lecturing. Check the shading on the brain stem. (00:05:55 - 00:09:35)
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: As the townspeople gather to storm the castle, the clock in the town square shows 10:30. When the Inspector steps out of the building to address them, the clock over his shoulder shows 10:00 PM. (01:28:45)
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: During his lecture on the brain, Professor Frankenstein draws the medulla oblongata on the black-board twice. (00:05:45)
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.
Answer: It's called "Transylvanian Lullaby" (as they tell you in the film) and was composed for the movie.
Myridon