After Dutton lines up the shot in the scope to kill the deer, he tells his son to pull the trigger. Before he can do that, the barrel of the rifle moves an inch to the right and then he pulls the trigger. After such a movement, he would have had to line up the shot again. He doesn't, but manages to make a perfect kill anyhow, as indicated by the camera shot through the scope as it had been before the barrel moved to the right. That perfect shot would simply not have been possible.
While hunting, John asks if the rifle will kick. James replies that it will. When they fire the rifle there is clearly no recoil, indicating a light powder blank was used.
James brings a kill back to his campsite. As he talks with Shea, he throws a strip of venison over the fire. He continues his conversation with Shea and pulls a fully cooked piece of venison off the fire after only 90 seconds. Not even a microwave oven would have cooked that piece of meat that quickly, and the fire he cooked it over was a roaring fire, but a small campfire (which would have been good for slow cooking. It would have taken at least 5-10 minutes for each side of that strip of venison to have cooked it.
When James is teaching his son John how to hunt deer, a modern earplug is briefly seen in John's right ear when they are looking in the rifle scope.