Character mistake: When Melanie and Scarlett are talking with an (off-screen) wounded Confederate soldier, the soldier says he hasn't heard from his brother since Bull Run. Only Northerners refer to that battle as Bull Run; Southerners have always referred to it as Manassas.
Character mistake: David Niven and his father are playing chess, and to checkmate his father, David Niven makes two moves, which you absolutely can not do - the only time you can move 2 pieces is when you move your castle and the king at the same time (castling), but you can't do that when you are in check.
Character mistake: On the proclamation announcing a plebiscite on a proposed "monarchy", the adjective "monarchical" is misspelled "monarchial".