When Meek and Solomon ride off in pursuit of the Indian, Meek's hat blows off and he continues on without stopping. When the two men return some time later, with the bound Indian in tow, Meek is wearing his hat.
In the last shot of the scene when the Indian carves a picture into a rock, the previous carving has disappeared/changed.
The Indian is supposed to be a Cayuse and speaks the Downriver Nez Perce language, but some of the phrases he speaks are in Crow, a totally different language. (The actor who plays him has Crow and Cheyenne ancestry.)
In an early scene with the three women walking, there was abundant Russian thistle on the ground. The film was set in 1845, but Russian thistle (Salsola tragus) wasn't introduced to the United States until arriving in South Dakota in 1870 or 1874, as weed seed in flaxseed imported from Russia.
Early in the film, three women are walking across the baked desert following the wagons, presumably to the west. The guide may be off course but nobody would mistake east for west. Yet the women's shadows are to their left as they walk, and since the sun would always be in the southern sky in Oregon, they could only be walking east.