Continuity mistake: Just before the Breeders Cup the horse is upset and Kurt Russell puts his hands on either side of her face to see what she is "thinking". First his fingers are practically in her eyeball and when the shot changes his hand is back by her jaw. This happens to quickly to be a natural movement.
Other mistake: Although the film's story covers the better part of a year, Dakota Fanning's permanent upper frontal incisor (permanent tooth) is just beginning to emerge. At the end of the film. months and months later, her tooth is still just beginning to emerge.