Following the movie time line, Jack Crabbe should have been rescued from the Indians around 1865. When he enters his gunfighter period around 1866, Jack is carrying two 1873 Colt Peacemakers while Hickok's pistol is an 1882 Colt.
When Shadow That Comes In Sight rescues young Jack and Caroline after their parents were killed, you can see Caroline put her foot up to a stirrup as she mounts the horse behind Shadow. When she dismounts it appears that Shadow, like most other Cheyennes, rides bareback.
When Jack and Olga are being photographed in front of their store the photographer removes the lens cap to expose the film and we see the image being taken reversed on camera glass. In reality the film holder would have blocked any view during the exposure.
..or maybe not. If the movie is just a tall tale told by Jack Crabb, then most factual errors and anachronisms are simply the character's mistakes or quirks. However, since this is debatable, they are left on this list for your consideration.
During the credits at the beginning of the movie, young Jack comes out of hiding and looks at a man's body, with an arrow sticking up out of it. The top of the arrow moves slowly as the "dead" man breathes.
The goof items below may give away important plot points.
Custer's attack on the Cheyenne at the Washita River occurred in the winter of 1868. Since Wild Bill Hickok was shot in the summer of 1876, Jack's drunk period would have lasted about eight years. Also the Battle of Little Big Horn was on June 25, 1876; Hickok was killed August 2, 1876, more than one month later.
In the saloon scene where Wild Bill Hickok is killed (1876), there is a Miller beer "Girl on the Moon" picture on the wall. Although Miller beer started operations in 1855, the "Girl on the Moon" advertising was first used in 1907 and it wasn't the same picture as the one in the movie.
When Wild Bill Hickok is gunned down, he lives long enough to have a conversation with Jack Crabb about the Widow. The shooter is apprehended immediately, claiming Hickok killed his father. In reality Hickok was killed instantly by Jack McCall, who ran away and was later found hiding in a local butcher shop. McCall's claim was that Hickok killed his brother not his father. The film also neglects to depict an important part of the Hickok mythos: he died holding two aces and two 8s, the origin of the proverbial "dead man's hand." And as noted elsewhere, Hickok's fall occurred AFTER Custer's Last Stand, not before it.
In the film, Custer and many of his men are killed by arrows. By the time of the Battle of Little Big Horn, the Plains Indians realized that bows and arrows were obsolete, and the braves who wiped out Custer's command were armed with rifles, lances and tomahawks.