Other mistake: In the battle for Fredricksburg you can see streaks in the sky from jets.
Other mistake: In the Battle of Bull Run, you can see that they use the same shot twice. It is a wide panoramic shot of the two armies. You see two explosions, one in the middle, and the second by the tree on the right.
Other mistake: In the scene where Gen. Jackson leaves the bedroom of his sleeping wife and child, you can see a modern light switch covered over by a piece of plastic and paint near the door frame.
Answer: The nearest one I can find listed was at Kirksville in northern Missouri.