Revealing mistake: When Helga is sent flying into her room, the support cable that is attached to her is visible.
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: 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: 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)
Chosen answer: While no specific date is given, Mel Brooks wanted to do a tribute parody to the classic 1930's horror film, thus the Black and White film and the 30's style film techniques. However, Hans Delbrück (the brain Igor is suppose to steal) was a real-life person who died in 1929. Given that and the cars seen, it's a safe bet it's suppose to be set in the early 1930's.
Bishop73