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.
During the cavalry's first encounter with the Indians, the cannons are fired and there is absolutely no recoil.
A lot of confusion in the production design appears on the screen. The story represents the plains dwelling Cheyenne who want to leave their Oklahoma reservation for Wyoming. Yet much of the costuming appears to be Navajo and Apache. And the Monument Valley landscape has no relationship to Oklahoma.
Captain Wessels had ordered the door locked to the warehouse, after he went in to talk to the Indians. As he bangs on the door to be let out, the soldier opens it immediately. That would have taken at least 5 seconds to unlock.
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.
The Indians at the fort surrender but are allowed to keep their rifles, knives and war clubs.
The lanterns held by army guards outside the warehouse where the Indians were being kept after surrendering were "Coleman" lanterns, first produced in 1914.
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.
In various shots, most notably when we first see the cavalry outpost, jet contrails can be seen in the skies.
The Navajos travel 1500 miles but never seem to leave Monument Valley, except for some snow scenes.
There are no mountains in Nebraska. During the Fort Robinson sequence, mountains are visible, whereas Nebraska has no mountains.
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.
Where did the buried guns the Indians uncover come from.
They were brought by the cavalry. Guarded by the cavalry.
Nothing in the story explains where the came from.