Colonel Norton P. Chipman was actually a full Colonel, he had been promoted to this rank in the aftermath of the battle he alludes to, the Battle of Fort Donelson while in command of the Second Iowa Infantry. In this movie he wears the rank of Lieutenant Colonel, three years after having been promoted.
Early on, a captain played by Martin Sheen comes into the court to tell Gen. Wallace that the defendant tried to hurt himself. The crossed sabers insignia of the cavalry on Sheen's cap is upside down.
The two provost guards on duty during the trial are seen slouching, lounging about and generally taking the whole thing rather casually. It's not likely that the president of the court would allow that.
(at around 1 min) Boom mic bounces around quickly in the frame when the defendant starts losing his disposition in front of the court witnesses.
The character of Henry Wirz was referred to as Captain Wirz several times during the film. In reality, Wirz had been promoted to Major about two months before the end of the Civil War, and Major was his final commission. Wirz should have been referred to as Major throughout.