Continuity mistake: In the scene where the 54th is on parade, Shaw commands "eyes right" and looks to his right and points his sword down to the right. Then the next shot is a brief shot of his parents and then when they return to Shaw, his sword is pointing up in the normal marching position. There was no audible command to stop saluting.
Factual error: When Shaw tells a reporter how well his men did in battle, in the background you can the southern tune "The Bonnie Blue Flag with the Single Star" playing. It's a southern anthem, so wouldn't be played in a Union camp.
Continuity mistake: When Colonels Shaw and Montgomery are in Darien, Georgia, Montgomery shoots a soldier (apparently in the heart) for touching a white woman. When the troops are marching out of the town, the soldier who was shot has miraculously felt better, gotten back up and joined the ranks. (01:07:05 - 01:08:55)