After Harlow and Larchmont are done fighting, Julian refers to Harlow as "James Aloysius Harlow." The character's name is "James H. Harlow", as written on his telescope and mentioned by other members of the wagon train.
According to the movie, the land rush occurs during Ulysses S. Grant's presidency, which ran from 1869-1877. However, it shows a Pony Express rider delivering a message to Slade. The Pony Express existed from April 1860 to October 1861.
When Junior Ferguson jumps off the cliff into the water after Harlow falls, he hits the water mostly on his back. When the camera cuts to the crowd above and then back to the water, his feet are sticking up out of the water, implying that he'd gone head-first into the sandbar.
Julian fires a warning shot into Slade's belly, then he walks away. When the camera cuts to a close view from Slade's hip, you can see Julian quickly turn around moments before Slade reaches for his gun, too soon for this shot, as though he'd heard Slade pull his gun.
Julian fires his warning shot into Slade's belly, turns, and walks away. Then he fires twelve more times, without reloading, for a total of thirteen shots. That would be impossible with two 6-shot revolvers.
Near the end of the movie when the politician is making a speech encouraging the attendees that their future lies in the west, he gestures and points with his cane indicating the direction west. However based on the time given, high noon, (as indicated by the watch of the man with the starting pistol), the shadows on the ground clearly indicate that he is actually pointing east.