In the flashback scene, Tom Hanks plays General George Meade. He wears two stars of a major general at Antietam, September 17, 1862. Meade was ten weeks away from promotion to that rank. He would not be a major general until late November 1862. At Antietam, he wore the single star of a brigadier general.
In the flashback scene at the Battle of Antietam, James wakes up on the quiet battlefield, with the text saying it was the day of the battle, Sept. 17, 1862. Based on the level of daylight, it appears to be in the afternoon. There is no cannon fire or musketry heard, even though fighting was going on not far away in the Sunken Road, or perhaps to the south along the Ninth Corps front. At the very least, distant cannons, to say nothing of those closer, should have been heard.
General Meade's uniform and gloves are perfectly clean in the flashback as he sits with James. His division had been engaged in fighting the bloodiest day in American military history. Meade was simply not that clean in the afternoon at the Battle of Antietam.
Lee did not surrender at "Appomattox" but at Appomattox Court House, which was the actual name of the place.
Jim Courtwright was not the marshal of Fort Worth in 1883. He left in 1879 after losing his bid for reelection and returned in 1884 to establish a private detective agency.
When James Dutton arrives in Fort Worth he informs the livery that he is the owner of a Bay and a Buckskin. The horse he is referring to as a Buckskin is actually a Palomino (The horse that Elsa rides, "Lightning")
Brennan offers to pay $100 a month for cowboys. The modern-day equivalent is about $3,000, which far too much. To put things in contrast, 131 years the Yellowstone ranch hands were only paid less than half of that.
At 31:45 there is a Truck and trailer visible in the back ground, it's just to the right of the tree. Also on the far right side of the screen you can see a traffic cone.
At 35:20 a camera tripod is clearly visible.
At 23:35 Elsa Dutton recounts that 18 years prior Lee surrendered to Grant in the village of Appomattox; this is a common error. The town which Wilmer McLean's home existed was called Appomattox Court House, then the county seat of Appomattox county. The town currently named Appomattox was, at the time called Appomattox Station.