Factual error: Carter's war record says he won the Southern Cross of Honor during the American Civil War. While this medal was authorised, it was never actually awarded.
Suggested correction: John Carter isn't a real person either. This is science fiction, not a historical documentary.
It's still a valid point that he has a decoration that was never awarded. It's mostly science fiction, but the parts that take place in the real world are supposed to take place in the real world.
I think you're missing the point. The medal could have been awarded during that time, but no real person actually was awarded it. There's nothing preventing someone from being awarded it, and John Carter, as a fictional character, was awarded the medal. It would only be a mistake if they showed a real person who actually existed be awarded the medal or if the medal was never commissioned at that time.