When training Red to the sound of the starting bell, the first time Red took off by himself after first dumping Joel. He actually ran nearly to the far end of the field, but immediately afterward when Joel sent Daisy the dog to go fetch Red back, Red was standing peacefully just 10 yards or so away.
When Red raced Mr. Moresby's horse, he was made to appear as though he couldn't run on the inside against the rail of a circular track, as he had supposedly only ever previously raced straight-track racing at the county fair. However, it's plainly obvious that Red's head was being pulled to the right in the turns to keep him from running on the inside as a horse would instinctively do. Regardless of whether a horse had ever raced on a circular track or not, no horse would ever drift to the outside of a curve in a circular or oval track. Any animal would naturally stay to the inside of a long curve while running at full speed. This was a forced and artificial story line to add tension to the plot.
Obvious stunt double for Joel (Ted Donaldson) in the horse-riding sequences.
When Red is fighting the bear, the rope tying him in the brush is clearly visible.
The wire used to trip the horse during the bear attack is clearly visible.
In the Color Version when Red was being attacked by a bear, one quick scene was Black and White.
The dog is called Daisy in the credits, but everyone in the movie says Curly.