At minute 40:07 Pemberton and Buchanan encounter the bear. The bear that appears on screen is a grizzly, not a black bear. Grizzlies did not inhabit the Smoky Mountains of 1929.
On two occasions there are "Zippo" lighters shown and used. The movie takes place in 1929. The "Zippo" company was not founded until 1932 (per their website).
Serena places a tourniquet on Galloway's forearm which the audience is told saved his life. In reality, a tourniquet on the forearm wouldn't have stopped the bleeding due to the radial bones.
When George Pemberton throws down on Mr. Buchanan he doesn't have the hammer cocked on his rifle. Also, afterwards he says that Mr. Buchanan was in his cross hairs as though he was using a rifle scope and not open sights.