When Bill receives the letter regarding his son's illness the letter is dated the 20th of Aug. and after that date he receives an invitation for an event dated Aug. 15.
Early in the film, Sergeant Chips McGraw refers to Buffalo Bill's "big Springfield" rifle but Bill is armed with an 1866 Winchester rifle in this scene.
After Kit Carson Cody dies (in 1876) the attending doctor describes diphtheria as being caused by "a germ in the water system and sewerage." However, the first recorded instance of this disease being linked to unclean drinking wells was first published in the British Medical Journal in 1880. In the 1870s, in the USA, the real cause of the disease was still unknown.