Factual error: At the beginning of the movie they are flying in the balloon for several days. The wind is constantly blowing everything around, hair, clothes etc. I've been in a balloon. Since the wind is blowing the balloon, you are moving at the same speed as the wind, therefore, you don't feel any breeze or wind, it's dead calm.
Factual error: The balloon that the Union soldiers escape in has no mechanical burner of any type in it that would be needed to keep the craft aloft in the air. A balloon flies by heating the air inside the bag, causing it to rise up. It descend as it cools.
Suggested correction: Gas balloons (using Hydrogen or Helium) large enough to carry passengers were invented in the late 1700s. Gas-filled observation balloons (such as the one in this film) were, in fact, used during the Civil War.