In the scene in which Charlie Anderson talks to Colonel Fairchild about his mistakenly abducted son in the Union camp, there is clearly a white automobile being driven (from right to left) in the background.
The locomotive on the train that gets burned is equipped with air brakes, which were not invented until 1872. Although the locomotive is mostly filmed at such an angle that the air brake equipment is not visible, a connecting air hose can be seen on the front when the train is stopping for the fire on the track, and whenever the train is stopped, hissing noises from the air compressor can be heard.
The Andersons carry repeating rifles, which were available in the 1860s, but quite expensive, and also quite rare. However, the rifles carried in the movie are of a type (with a loading gate) not invented until 1866.
When Boy and Gabriel are found by the creek there is a young African-American soldier with the Union band. Then later Gabriel, a young African-American boy, is seen fighting along side Union troops. Free Blacks and former slaves did not integrate into Union regiments, but instead, served in all-Negro regiments.
In the battle where Boy is wounded, the manner in which the Confederate soldier loads his weapon is wrong. He would have used paper cartridges, not separate powder and ball. Unless carrying a personally owned weapon (which he is obviously not), a soldier would not even have a powder flask.
Just as the fight is ending, and Mr. Carroll is about to shoot Pa Anderson with his gun, you see the Boy in the water trough about to make an attempt to grab him. However, the actor pulls back at the last minute, obviously aware that his attempt to grab Carroll is mis-timed when Jenny shoots the gun out of his hand.