The U.S. Cavalry Troops are displaying a Confederate flag. The story was supposed to be in January 1861. The version of the Confederate flag displayed was not even in existence even in the Confederacy yet.
Whitlock misuses the term "copperhead" as describing a member of the Union who is secretly working with the Confederacy. In fact, the word meant Northerners who were opposed to the Civil War.
In the cavalry train that leaves Fort Union for Fort Stanton there is a wagon transporting Marcy Whitlock that is marked with the letters US MD and a red cross. The red cross symbol was created in Geneva in 1863 and not in use with the US forces in 1861.
Towards the end of the movie an army convoy has camped for the night. In the background a soldier is playing "Beautiful Dreamer" on a harmonica. Stephen Foster had not yet written the song and it wasn't published until 4 years after the 1861 time-frame of the story.