During the train robbery sequence at the end of the film, the train consisted of a caboose, two flat cars, and two passenger cars. During the gun fight, the two flatcars and the caboose are separated from the rest of he train. However, the other half of the train consists of only the coal car and the engine. The passenger cars are missing. They reappear later when the train is derailed.
When the buffalo hunters arrive on the Union Pacific, the steam locomotive is a wood burning loco, recognized by its large, funnel-shaped smoke stack which contains a spark arrestor. Such locomotives were used by the Central Pacific, which only had access to wood as a fuel before the First Transcontinental Railroad was completed. In contrast, the Union Pacific used coal, which was easily available to them not the least from from the fields in the Rockies, while it had little access to trees for fuel on the plains and in the mountains. Its coal burning locomotives had long straight smoke stacks without spark arrestors.
When the wagon train on its way to California is attacked by Indians, it is in a mountainous area, yet the Indians are identified as Cheyenne. The Cheyenne tribe was a Great Plains tribe, and would not have been that far west.
The Prescotts are floating downstream on a raft when they "take the wrong fork of a river." But that's impossible since tributaries flow into the main branch of river when headed downstream, not away from it.
There is no explanation of why Sheriff Ramsey is fine in one scene and wearing a bandage on his forehead in the next, immediately following. (there was a deleted or unfilmed scene where Zeb knocked Ramsey out when the Sheriff tried to stop him from going after the train robbers).