Audio problem: The Rabbi's horse is bucking in reaction to the rattlesnake, and all the while the Rabbi is yelling in Yiddish - but his mouth is not moving.
Factual error: The movie takes place in 1850-51, and yet when the Rabbi is challenged to a shootout in San Francisco, the weapon he is handed is an 1858 Remington New Model Army revolver.
Other mistake: When Harrison Ford and Gene Wilder are being chased by the bad guys, they're discussing whether the sun is setting, and there is a shot of the sun going behind a ridge. When the actors are shown again they are in full light, and not in shadow as they would be if the sun was going down, even though Gene is bobbing up and down as if he's making the sun go higher or lower by the position of his head. (This is so that they can remount once the sun has gone down, as the Jewish day of rest will have ended.)
Factual error: The rabbi, Avram, shows his partner, Tommy, a photograph of his betrothed. However, in 1850-51, it would not have been on photographic paper, but either a tintype or a daguerreotype, on metal or glass.
Factual error: The entire sequence where the two heroes have to walk rather than ride to escape the posse because it is the Sabbath is completely false. There is a reasonable chance that their lives are in danger from the posse. According to Jewish law, it is forbidden to risk one's life for the Sabbath. In that situation, not only would they be permitted to ride, they would be compelled to. There is no way the rabbi would not know this basic principle.
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.
Factual error: The locomotive used by the M&O R.R. is a coal-burner, a fuel not employed in locomotive fireboxes until the late 1860s, when bituminous coal mines became prevalent.
Continuity mistake: While pointing his pistol at Matt Diggs, the Rabbi cocks the pistol's hammer. A split second later from another angle, the pistol's hammer is down.
Answer: Right on the nose.