On the evening of Lincoln's assassination Van Ellyn and his associates are discussing the supposedly then current John Soule editorial, "Go West, Young Man." Lincoln was murdered in 1865. Soule wrote that famous line in 1851.
According to the film, Custer's Last Stand and the establishment of the boom town of Deadwood occur shortly after the end of the Civil War in 1865. In actuality they happened 11 years later in 1876.
Abraham Lincoln leaves for the theatre, and is shot within a matter of minutes. In reality, it was two hours between Lincoln's arrival and assassination.
Sec. of State William H. Seward was not present at the cabinet meeting that morning, he was in his bed, recovering from injuries sustained in a carriage accident (and later that night conspirator Lewis Powell attacked and stabbed him, but he survived).
The repeating rifle is shown as being introduced in 1865, after the end of the Civil War. We are told that the soldiers would have been glad to have them. In fact, the rifle was invented earlier and was used during the war.
During the riverboat card game scene, Bill Hickock, who "doesn't like women" is clearly wearing a wedding band.