At one point, Creighton says "...we'll be hitting the hills" as the telegraph crew heads west from what was then called Omaha City. This is incorrect. Omaha was notorious for being hilly (in the late 19th Century and early 20th, the city went to great efforts to level many of the hills), but as you move west, away from the Missouri River, near what is now about 84th Street in Omaha, the land begins to flatten out dramatically.
During one of the scenes in the then (referring to the time period of the story) non-existent town of North Platte, an Army officer refers to a Fort "Kerny." The fort, and the subsequent town, are pronounced "Karney."
In the opening sequence, Vance Shaw escapes a posse by riding through a herd of grazing wild buffalo. But in close-ups of the beasts, cowboys herding them can be seen in the background, despite no such cowhands in the establishing long shots of the herd.
The goof item below may give away important plot points.
In the gunfight at the barbershop, Shaw first fires
shots with his right gun, throws it away and then uses his left gun. He then fires at least nine shots with this gun without reloading it before the end of the gunfight.