About a third of the way through the movie, when the "white" guys charge the Indians, their charge takes them across virgin sand. Except for the track of what is clearly a modern car (tread marks clearly visible) across their path.
The Cheyenne Indians cross the Canadian River in Indian Territory, which today is known as Oklahoma. The film was shot in Utah, where the magnificent desert bluffs and mountains in the scene exist. Nothing along the Canadian River in Oklahoma even closely resembles this. The Canadian River flows through prairie and is lined by cottonwood and other trees.
The language used by the Cheyenne in this movie is not Cheyenne. It is Navajo. Cheyenne is an Algonquian language, whereas Navajo is Athabaskan (Na Dene), and they do not sound even remotely similar. This is explainable, however, by the fact that this film was shot on the Navajo Nation.
When Secretary of the Interior Carl Schurz talks with the colonel at the Victory Cave, the soldiers standing in the background are from a totally different scene: the light, colors and proportions are different.