Revealing mistake: When McKay and Ramon are riding into Blanco Canyon to rescue Julie, you can see a diesel loading shovel with its bucket raised in the bottom of the frame of one of the scenic shots. Presumably the scene was shot in a quarry and they didn't get all the equipment out.
Continuity mistake: When Jim tries to ride "old Thunder" he bucks off and brushes all the straw out of his hair. Seconds later it is back.
