Character mistake: Ryan's final diary entry says the US Cavalry fought against "French irregulars." The French lancers were actually regular troops.
Factual error: The US Cavalry are careful not to run into Confederate cavalry from Fort Davis, who are shown in the distance. Fort Davis was indeed occupied by the Confederates from 1861 to 1862, but was then abandoned until 1867. The film is set in 1864, so there would be no Confederate troops at Fort Davis.