Other mistake: At the beginning after Dunbar leaves the surgery area, he walks up to fence where a soldier is lying down. Next to him is an apple with the grocery sticker on it. (04:49:00)
Other mistake: Dunbar has to race back to the fort in the middle of having a shave. The amount of soap on his face alters shot to shot.
Answer: He shaved it as he began spending more time with the Lakota. Native American tribes rarely accepted facial hair. As you can see, none of the other Lakota men have any. He also grew his hair longer as an abandonment of his military lifestyle.