Revealing mistake: In the classroom Frederick stabs himself in the leg with a scalpel. Look closely and you can see the thick pad covering his thigh inside his trouser leg. (00:11:10)
Revealing mistake: One of Peter Boyle's teeth on his lower jaw was painted black for that "broken grin" look. It can be seen reflecting in some scenes: when Frankenstein enters the cell with the monster and it cries, and later when the monster screams while killing the jailer. (01:15:30 - 01:28:40)
Revealing mistake: For most of the opera house stage presentation, the monster is a full head taller than Friedrich. During the tap dance, however, they're the same height. Although the camera angle/depth of field used tries to disguise this by keeping Gene Wilder in the foreground for most of the shots, it's still apparent that Peter Boyle isn't wearing his probably-impossible-to-dance-in platform shoes during the sequence. (01:24:00)
Revealing mistake: When Helga is sent flying into her room, the support cable that is attached to her is visible.
Answer: It's called "Transylvanian Lullaby" (as they tell you in the film) and was composed for the movie.
Myridon