Revealing mistake: Although the film is set during the aftermath of the Mexican War (1848-50), the mountain vistas display some lovely radio towers and fire ranger stations.
Other mistake: During the ‘rescue' mission to save the trapped wagon train, none of the riders are carrying packs of food or any supplies. One man is carrying a military unit banner on a pole. Unrealistic for this type of activity.
Continuity mistake: Jeremiah Johnson acquires two horses at the beginning of the movie, one completely black, and one almost completely brown. A few minutes later, Jeremiah Johnson is seen riding a horse that is different than the two he just acquired. The new horse is distinguished by his near entirely white face. (00:07:20)
Factual error: The crazy lady, whose family (except the boy), were murdered by Indians, sings "Shall we gather at the river" after Jeremiah buries them. Only that wasn't written until 1864.
Continuity mistake: When Johnson stops with the rescue party at the edge of the Crow burial grounds, the view of the grounds and the close ups of the conversation between the characters have extremely inconsistent snowfall, in some instances very heavy and the next edit, nothing.