Revealing mistake: There is one shot where the camera shows the battlefield with a large tree in the middle of it. You can see that the tree has been cut away to make room for a power line, which has been removed for the movie.
Factual error: There is one minor anachronism in the scene in which several Confederate officers are discussing politics with the British officer, Freemantle, while playing cards near a campfire. General Pickett is seen holding some paper money in one hand. The only note visible is a Confederate twenty dollar bill, with the back of the note exposed. While the note appears to be genuine, the back design is unique to Confederate twenty dollar bills issued after February 17, 1864 - more than seven months after the battle.
Character mistake: When Buster gets hit in the arm the first time, he is busy tying the kerchief below the wound. (02:21:05)
Continuity mistake: At the beginning of the movie when the scout is talking with Longstreet, when the scout holds up his finger and says "you didn't know they were on the move out there", a long stream of troops is seen marching to the right. When the shot cuts to Longstreet then back, they have disappeared. (00:09:55)
Factual error: As Buford's Cavalry is approaching Gettysburg there is a scene filmed from behind as Buford stops by a fence and peers out over some fields. One of the fields appears to be a corn field and the corn appears to be about 5 to 6 feet high, much too high for June 30th in that part of the country. Having been raised on a farm in New Jersey corn that was "knee high on the 4th of July" was considered a bumper crop. The height of the corn was much higher than "knee high" on what was suppose to be June 30.
Visible crew/equipment: During the scene when the confederate regiment begins to move up little round top, right after the "7-8 bullets shoved down the barrel line", a audio technician and boom mic can be seen to the left side of the image hiding in the trees. (01:57:15 - 01:57:50)
Continuity mistake: There's one scene wherein Chamberlain is on the move wearing the shoulder straps of a lieutenant colonel and then, shortly later, with no explanation, on the same day, he's wearing the shoulder straps of a full colonel.
Character mistake: Chamberlain's sidearm is a Colt Army .44, which uses a peg to secure the barrel to the cylinder axle. During the fight, Chamberlain replaces the empty cylinder with a fresh one, pushes the barrel against a log to seat it, but never shoves the peg in. A loose barrel might well result in a misalignment of that barrel with the chamber being fired, which would blow the barrel off the weapon.
Factual error: Pickett's charge moved from west to east and was made about 2 o'clock in the afternoon. When Pickett rides down the line to encourage his men before the attack, it is clear from the shadows that the scene was filmed early in the morning.
Continuity mistake: The mane on Lee's favorite horse, Traveler, changes from gray to white to gray.
Factual error: During the scene when Gen. Lee is talking to Moxley Sorrel in the cabin AFTER little round top, he calls Moxley "major", and moxley is wearing the insignia of a Confederate lieutenant-Colonel. By that date in the war he was a lieutenant-colonel, but a couple times Lee calls him major.
Answer: Yes. After the 2nd Maine Infantry was disbanded, there were 120 men with 1-year of service left. They mutinied because they said they only agreed to fight under the 2nd Maine flag and the Army disagreed. So they were marched under guard to the 20th Maine, led by Chamberlain. Chamberlain was able to convince most of them to fight, even though he was ordered to shoot any who did not fight.
Bishop73
Is there a reason why a few of them refused to fight?
Yes. The same reason why they mutinied.