Audio problem: When the Monster is tap-dancing to "Puttin' on the Ritz", the motion of his legs and feet do not correspond to the sound of the tap-dancing.
Plot hole: Kemp, after visiting the castle, would've assured the people that Dr. F. Was not making a monster. So, why is that guy boarding up his house if he has no evidence that a monster even exists? Even if he did tell them that he believes that Dr. F. Was creating a monster, how did the guy know that it had escaped? Also, he says that he remembers the last time. He wasn't old enough to remember something that someone else's grandfather did.
Other mistake: When they are removing the casket from the grave, the grave is just slightly bigger than it. How did they get underneath?
Audio problem: At the end of the movie when The Monster is shaking hands with Inspector Kemp, he pulls his prosthetic arm off. Inspector Kemp is heard saying, "Oh shit," however his mouth says just "Oh."
Continuity mistake: The blind man reaches for the cigars, and when the angle changes, half a second later, the broken pieces of the mug have changed position and have also increased and suddenly appear scattered all over the table.
Continuity mistake: Frankie arrives at the door of the blind man, who welcomes him. Then there's a close-up of the monster from a bit far away where you can see his shirt and head as if he were alone; however, a frame later the blind man is right next to him, his head almost touching the monster's.
Answer: It's called "Transylvanian Lullaby" (as they tell you in the film) and was composed for the movie.
Myridon