When Hostetler and Samuel Fields are by the campfire while searching for the horse, Hostetler rolls away from the fire and pulls his jacket up over his shoulder and most of his back as a blanket. When the camera angle changes to Samuel, and then back to Hostetler, his jacket is now under his arm and barely covering his back.
In the scene in Tom Nuttal's saloon, after William is trampled by the horse, Steve is drinking from a bottle of Bulleit bourbon. That bottle design was not introduced until 1987.
In Tom Nuttall's Saloon, Steve drinks from a bottle of Bulleit Bourbon Whiskey. Bulleit Kentucky whiskey was produced from 1830-1860, then not again until 1987. It would have been unavailable from 1876-77 when the show takes place.