As Bannon finishes shaving his face has remnants of shaving cream clearly visible, and he tells Nita to get him a drink. When she steps away the camera angle changes, showing his face clean, with no splotches of shaving cream.
There actually was a Ghost Dance movement; it was a religious revival of Native Americans in 1890, but it did not involve Apaches, who inhabited mainly the Southwest (Texas, Arizona, New Mexico). It was popular among the Lakota (Sioux) of the Northern Plains.
Each soldier carried a "Mills" cartridge belt around his waist, but no one carries any ammunition in them.
Katy Jurado still speaks in her real-life Mexican accent despite the fact that her character, Nita, is an Apache Indian living in Arizona. Her accent should sound more like a Native American accent, not Mexican accent.