Character mistake: In the scene where Quigley engages Marsten's men who are attacking the Aborigines, we see a man hit by a bullet and fall from his horse, then we hear the report of Quigley's rifle. When the man who gets away reports to Marsten, he estimates the range at three-quarters of a mile maybe. Marsten asks him how long after the bullet struck before he heard the report of the rifle. He answers two maybe three seconds. While this scenario would be plausible for a more modern high-powered cartridge like the .30-06, it is not accurate for the .45 2-7/8 Sharps Quigley is using. That cartridge loaded with 110 grains of black powder will propel a 540-grain bullet (best case) at around 1475 feet per second. Since the bullet is supersonic when it leaves the muzzle it will indeed precede the sound of the weapon's discharge for short distance. But not by very much and not for very long. The bullet goes transonic in about 400 yards and the the sound waves catch up to the bullet a little beyond 600 yards. After that, the rifle's report, travelling at a constant speed, gets progressively further AHEAD of the bullet which is gradually slowing. At three-quarters of a mile (1320 yards) the bullet's time of flight is about four seconds, while sound waves travel that same distance in three-and-a-half seconds. The man should have been struck at nearly the same time as, or up to half-second AFTER the report, depending on the actual range.
Character mistake: At the ravine, upon learning that the bridge doesn't exist yet, Marty states to Doc "We can't wait a year and a half for this to be built". If you carefully look at the sign, it says the bridge is opening Summer 1886. That's under a year away, not a year and a half from Sept. 1885.
Character mistake: In the opening scene when the bandit is going for his trigger finger, Billy is seen with his eyes slightly open in the background. His eyes are then shown to open suddenly with dramatic effect. (00:05:50)