The American Flag shown at the end credits, appears to have 36 stars (6x6). At the beginning of the of the Civil War (April 1861), the official US Flag would have had 33 stars (5 rows x 7 columns with one missing on either end of the middle row). The flag did change (July 4th, 1861) to 34 stars (one star added to the middle row) in July to reflect the addition of Kansas (January 29th, 1861.
Though the Pony Express ran during the time period of the story it never ran up to Wyoming and so would not be delivering news about the attack on Ft Summter.
The Southern soldiers sing The Battle Hymn of the Republic during the first day of the Civil War starting during the film. This would not be possible since the war started in April of 1861, and the words to the song were not written until November of the same year.
When the soldiers are floating the rafts downstream, there is very little apparent current. The rafts are moving faster than the current since water is splashing over the front of the raft and this can only happen when a craft is being propelled by something else. There are no oars or paddles on the rafts, so they are being towed by another boat. At times you can see ripple marks ahead of the rafts from the boat that is towing them.
When the Indians attack the troops on the rafts in the river, the same 2 Indians are seen being shot off their horses twice.
When the sergeant is crawling through the Indian lines to reach the trapped ex-soldiers, he stabs 2 Indians. Each time he can be seen stabbing the dirt beside them, and Indians getting through the fire lines are stabbed the same way, in the dirt beside them.
When a soldier takes an Indian spear in the gut for his commanding officer, after he is on his back on the ground, the spear he had been holding to his stomach is removed and it's clear it was never sticking in him, that he was just holding it there.
Even though the movie is set during the first few months after the beginning of the Civil War, some of the Indians are clearly carrying Winchester Model 1892 carbine rifles.