Other mistake: When Dr. F. is introducing the Monster in the theatre, he says, "as incredulous as it seems." "Incredulous" means unable to believe. The word he should have used is "incredible", which means unable to be believed.
Other mistake: When they are removing the casket from the grave, the grave is just slightly bigger than it. How did they get underneath?
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