The US Cavalrymen in Hostiles are armed with 1859 model Sharps carbines. This is a Civil War era weapon that was long obsolete by 1892, when the film is set.
The reporter takes a photo of the soldiers and natives before they leave the fort, He uses flash powder during the exposure but this would have had no practical effect against the bright New Mexico sunshine.
At one point the lieutenant addresses the sergeant major as "sir". A West Point officer would never address a non-commissioned officer as "sir."
Capt. Joseph J. Blocker is reading Julius Caesar early on and initially he's holding the book, its on the table in the next shot and back in his hand the shot after that.
Beginning in the 1840s, the Cheyenne and Comanche tribes were allies. The Comanche would not have tried to kill Cheyennes escorted by the Army, but perhaps tried to release them. It's a moot point, however as by 1892 both tribes had finished with warfare, both inter-tribal and against the whites.
There is a single African-American soldier, Corporal Henry Woodson, in an otherwise White cavalry regiment. The only Black cavalrymen in the regular army were in the 9th and 10th regiments, where only the officers were White.
By 1892, The Comanche were living in reservations in Oklahoma. Quanah Parker had taken the last of the Comanche to the reservation nearly 10 years before.
There would have been no hostile Native Americans on any route from New Mexico to Montana by 1892.The majority of "hostiles" were either on reservations by that time or deceased. The reason why, decades earlier, the Goodnight Loving trail went to New Mexico before turning north was because there were no Comanche west of the Texas panhandle.
At one point the trail they are traveling along becomes visible to the audience. It is clear that the trail was made by vehicles with bigger tires than those of a horse-drawn carriage.
At 53.12 minutes into the film the spurs on the boots on the deceased Cavalry Trooper are on backwards.
The pack train, which keeps appearing and disappearing, consists of two horses that seem to be loaded with a couple of sacks of flour apiece. Yet they produce all the appurtenances of camp life, including at least seven tents as well as folding tables and chairs, in addition to manacles and chains, picks and shovels, and anything else that comes in handy for the plot.
When Mrs. Quaid is shooting the dead Comanche she continues pulling the trigger after she runs out of bullets. On the first empty chamber the gun still recoils as if a shot had been fired.
Yellow Hawk's dead body is first shown wrapped in a blanket shroud exposed on an excarnation platform and then buried shortly later though exposure to the elements, birds and flies would be expected to take a much longer time to rot the flesh from the bones. Adjacent exposure platforms show neither enshrouded bodies on the platforms nor skeletons under the platforms.
Cyrus Lounde, the land owner who disliked natives enough to go against a presidential order, would have desecrated any other bodies that were placed in the ritual bural grounds... whether by burning the bodies or digging a deep mass grave and placing them there.