When Batouche spots the Cree and Sioux following, he sees them by looking down from a high point. However, when O'Rourke looks at them through the binoculars he sees them from front on, at ground level.
The Northwest Mounted Police did not fight any battles with the Sioux. In fact the Sioux foray into Canada after Custer's Last Stand was quite peaceful.
Sioux chief Crazy Horse did not flee to Canada after Custer's Last Stand. After the Battle of Little Bighorn, Crazy Horse led his band to the Tongue River area in Montana. Sitting Bull did lead his band to Canada.
The film is set in 1876 but the Stetsons worn by the Mounties were not introduced until 1904 (apart from those issued to the contingent sent to England for Queen Victoria's Diamond Jubilee in 1897). In 1876, the Mounties wore pith helmets in summer and fur "wedge" caps in winter, with pill-box caps for duties in forts and around summer campsites.
There are no mountains in Saskatchewan.
Movie is titled Saskatchewan but that province does not have the Rocky Mountains which dominate this film. Prettier, yes, but not factual, as the film was supposed to be based on a true story.
Shelley Winters asks the Mountie guarding the jail in Fort Walsh, Saskatchewan how far the fort is from Montana. The guard answers "the border is about 18 to 20 miles south of here". The U.S. border is about 40 miles (65 km) south of Fort Walsh.
At about 47:00, Grace (Shelley Winters) learns that O'Rourke's (Alan Ladd) first name is "Thomas". But at about 1:04:00 into the film, Grace calls O'Rourke "Tomlin".