During one of the first times Katy mounts Flicka to ride her around, Flicka isn't wearing a bridle. Then there's suddenly a bridle visible.
Near the end of the movie, after Flicka has been attacked, there are no visible patches of hair missing or scars from the mountain lion. Earlier in the movie when Katy finds Flicka, there are patches of hair missing where Flicka later gets attacked.
When Flicka is attacked, it's pouring rain. Then, when the camera zooms in on Flicka's head, everything is dry.
The license plates on the vehicles have the wrong county numbers on them. In Wyoming the number before the bucking horse indicates the county the car is registered in. For instances the horse trailer has County 3 plates on them. County 3 is in northern Wyoming, while they are based in southern Wyoming which would be either county 2 or county 5.
The Never Summer Mountains, referenced in the very beginning of the film, are in Colorado, not Wyoming.