Character mistake: Gene Wilder as the rabbi leaves the Torah on the floor of the porch of the home of the synagogue president. A rabbi would never put a Torah on the ground.
Factual error: In the wedding reception scene toward the end of the movie, the celebrants are dancing in a circle to Hava Nagilah. The song did not exist in the 1800s. The song is derived from a slow dirge from the early 1800s in Ukraine and was not written as the fast, energetic folk tune we know until around 1918.
Answer: Right on the nose.