Deliberate mistake: When the two Confederate and Union soldiers meet across the river and trade coffee/tobacco, you can see the other side of the bank behind them. It looks at least 50 feet away, yet before they were able to talk to each other without shouting. Also, the Union soldier raises the pipe to his mouth in his right hand, which switches to his left in the next shot. There is also a mist present at the beginning and end of the meeting, but not in the middle. (00:37:55)
Deliberate mistake: At Fredricksburg, when the troops from the 20th Maine are retreating, Tom Chamberlain is seen firing his revolver at the Confederates, and there is no burst of smoke, nor any recoil (also, the tip of the barrel of the pistol is off-screen.) This is because he is dry-firing the gun, since that shot contains dialogue and a real shot would interfere with the microphones. This mistake occurs earlier as well, with the Irish Confederate officer firing his revolver at the Irish Union soldiers, though no bullets are visible in the chambers, and the smoke from the primer caps is missing.
Answer: Pride, honor, and respect were some of the characteristics of a Southerner's perspective during the Civil War, and did not change through the war. At this point of the war, however, the Confederates knew they were now on the defensive, no longer fighting for either slavery or states' rights, but the survival of their land, farms, and homes against foreign invaders (Union troops) who were using "scorched earth" tactics to break the South's will and ability to fight. That alone, kept them fighting even though victory was not going to happen for them.
What are scorched earth tactics?
Destruction of farms, crops, livestock. Also destroy every town that the Union troops arrive at.