Factual error: When Lt. Dunbar gets to the Fort, they show a dove in the rafters. It is a domestic Ringed Turtle-Dove or domesticated Barbary (African Collared) Dove. They likely did not have those doves at the Fort, but rather should have been a Mourning Dove. Rock Doves and chickens were common domestic animals brought for food.
Continuity mistake: When Dunbar 1st finds a bloodied Stands with a Fist mourning on the prairie she has long hair extensions. When he carries her back to the tribe her hair is shoulder length.
Continuity mistake: The Civil War battle scene has trees already turning fall colors, and the cornfield is already showing frost damage with dying top leaves. The likely timing for scenery such as this would be about mid to late September. There wouldn't be enough time for Dunbar's leg to heal, then travel 1000 miles west, then establish rapport with the Sioux, then go on a buffalo hunt, then move to winter quarters before snow flies.
Revealing mistake: Costner is supposed to be nude after he gets out of the water and is watching Kicking Bird wandering around in his camp; however, a close look in the lower left of the scene will show Costner is wearing skin-colored panty hose. The elastic waist band is quite visible, cropping didn't get it all out. (00:54:20)
Factual error: In a scene where Dunbar is at the fort and a Henry 1860 rifle is lying on a firing port, there appears to be a long cartridge similar to 45/70 or.50 Govt with the rifle. The Henry 1860 rifle at the time used .44 Henry cartridges which were significantly shorter. (00:41:55)
Factual error: When Dunbar is leaving for his assignment, the officer holds a gun to his head to commit suicide. He's facing the camera with the gun screen left and a window screen right. If he shoots himself in the head from that position as implied, the bullet would have gone through his head and blown out the window, which the viewer sees intact after the shot when Dunbar looks back at the sound.
Factual error: When Dunbar saves the native American boy from the charging injured buffalo he jumps off, asks if he's all right then makes two repeated shots from his Henry rifle without cocking the lever. Only special safari guns did that, at a later date.