Visible crew/equipment: After Cloud Dancing leaves to search for the root and Dr. Mike gets the medication for Sully's pain, when it cuts to Jake and Birch talking inside the barbershop, the reflection of filming equipment is visible on the windows. (00:16:50)
Revealing mistake: When Rankin is gored by the white buffalo, in his last closeup the wood plank and steel posts are visible at the back of the animal head prop, at the right side of the screen. (00:44:30)
Answer: A Cooper was someone who made various things out of wood including wooden caskets and even barrels.