The Shetland pony Tucker (Dustin Hoffman) had to be painted brown during filming because his real coat turned grey. Everyone was so surprised, but the animal trainers did a little touch-up with brown dye.
As Nolan Walsh comes around the turn of his newly made corn field track and climbs off his tractor, there are no corn stalks on the ground. In the far shot of Channing hugging him, the ground is littered with stalks.
While Trenton's Pride is a foal, his blaze doesn't reach all of the way down to his muzzle. When he is grown up, it is past his muzzle. Horses' markings don't change that dramatically.
When Sir Trenton first sees his son racing Stripes, his owner/carer has just started to undo his rug and does not appear to undo the front two straps. When he rears, the front two straps appear to be undone as the rug slips straight off his body.