When Zeb rides up to the Arapaho and they fire at him, he races back to the train camp, gets off his horse and hits it on the rump. It races off, but after the buffalo go through the camp and Zeb is ready to leave, his horse is neatly tied to the fence.
Rawlings is traveling up the Ohio river to Pittsburgh with the Prescott family down river. All are together the first night, with each leaving the next morning to continue their own directions. Yet, Rawlings reaches the pirates cave and then the Prescotts reach it, with both going in separate directions. How did they manage that?
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 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.
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.
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).
Linus and Eve die three years apart, yet both their graves look fresh when Zeb comes back from the war. Although the grave of Linus is empty, so it and the headstone may have been placed at the same time Eve's grave was dug.
During the last sequence in the rapids, when the raft disappears under water, there is a sharp edit cut to make it look like the raft never resurfaced. You can tell, as the waves and spray suddenly change.