When General Crook is telling E.B. that he should work with Captain Bubb for the troops "logistical needs", he points at the Captain with his left hand across his body. When the camera angle changes to behind the General, he is pointing at Captain Bubb with his right arm extended straight out.
Captain Bubb wears black leather boots with large zippers on the sides. Zippers weren't invented until 1893 - twenty years later.
When the troops are mustering to leave Deadwood towards the end of the episode, the bugle fanfare is heard uninterrupted throughout the camp, even though we can clearly see the bugle player has the instrument away from his mouth for a short while.
In the first scene, after Dan hands Al his morning coffee, Dan walks under the shadow of silk screen frame, a piece of lighting equipment used to diffuse the sunlight. The tell-tale outline of a C-stand adjustment screw passes over his chest.
When Merrick removes the lens cap while taking a photo of the cavalry officers; he loses his grip of the lens cap and it remains in front of the lens. Since photographs taken in this way required a long exposure a mistake like this would have resulted in ruined picture. The picture that Merrick later laments about and hopes to re-shoot shows no evidence of the lens cap that was in the way earlier.