When Grace is watching the show jumping, the commentator says "Pilgrim moves with absolute confidence at the command of Ms. McLean." This makes it clear that it is Grace and Pilgrim jumping. However, the Pilgrim on the TV is a bay with a white blaze. The Pilgrim throughout the film is chestnut with a small white star.
When Booker first goes to see the horse at the hotel and it runs out of the barn it has a big white blaze that covers most of the face, but in subsequent shots it has only a small star on the forehead.
When Tom goes the motel to see the horse, his hat changes styles between shots.
When Tom is sitting in the tall grass after being dunked in the creek, his shirt is dry, but later the shirt is wet again.
When Gulliver falls, it is clear that he damages his fetlock (ankle) badly. Once he is on the road his fetlock seems to be fine.
Although the opening scenes are set in winter, Pilgrim has a light summer coat which is impossible at that time of year. In reality the scenes were filmed in May.
When the girls go riding, at the start of the film, it is cold enough to snow yet their breath is not visible.
Booker is in the corral alone trying to "hook on" with Pilgrim. Just before he squats to remove the lasso from Pilgrim if you look under the horses neck you can see the lower half of a man dressed exactly the same as Booker.
When Tom is teaching Grace to drive the pickup, the gearshift remains in "park" the entire time.
When Pilgrim is shown rearing up at the semi, a lunge whip can be seen in the shot flashing by his head.
As Pilgrim rears up when Liz the vet approaches him in the tunnel, a whip is briefly seen in the lower right hand corner.
In an early scene, a phone call is placed from Manhattan to the suburbs. The audible touch-tone sequence is seven digits. Since the NYC metro area has many area codes, ten-digit dialing is mandatory there.
Robert arrives at the ranch in a rental car, but needs a ride back to the airport.