Factual error: When Morgan Freeman is helping hand out rifles to the recruits, he is reading off the serial numbers. Enfield rifles of the Civil War era did not have serial numbers.
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.
Suggested correction: The tune is correct; however, Union soldiers made their own words to the song.