At he beginning of the horse-breaking scene the horse's hair is a mess and covered in mud. Once the horse is lassoed, the horse is suddenly clean and brushed. At the conclusion of the scene, as it runs away, the horse is muddy again.
The rifle Steve McQueen uses in the film is a Winchester Model 1876, stated to be chambered in .45-60 Winchester, however, the rifle was actually chambered in .45-75 Winchester. The real life Tom Horn carried a Winchester Model 1894 chambered in .30-30 Winchester.