Cyclone, the gray racehorse, changes from a soft pale gray, to a dappled gray, to a very dark gray with a white tail throughout the match race.
The layout of the cards in the solitaire game Henry is playing while talking to Alec changes from shot to shot.
The blanket can be seen in Mother's hand while she is thanking horse after she has already put it on Alex.
Throughout the movie, the Black Stallion is an Arabian, but during the match race scene, the horse that Alec is riding is a dark bay Thoroughbred.
Whan Alec puts the seaweed out for The Black, Alec is first seen near the water, then further away, then closer to the cliff.
When Alec encounters the cobra, the sheet of glass that separates them is visible - there is dirt on the glass parallel to Alec's left shoulder.
The white star on Cass Ole's forehead as well as the white socks on his legs are faintly visible through the black dye in some of the scenes of him running along the beach.
(at around 16 mins) When the horse jumps off from the deck of a sinking ship, its forelegs are seen to touch the solid ground leveled at the same height as the ship's deck, thus revealing it is not sea surface.
Early in the film Alec's father is playing cards with other men. The coins on the table include British large pennies with Queen Elizabeth II on them. The film is set in 1946 and Queen Elizabeth began appearing on coins in 1953.
As the horse runs down Alec's street with Alec chasing him, after the red car pulls over, a contemporary (i.e. black with white background) "Speed Limit 25" sign can be seen. Most speed limit signs then were black background with white lettering and would have read something like "Speed Limit 25 Miles".
The horse statue on Alec's nightstand was one made by Breyer Animal Creations in the late 1970's shortly before the movie came out. The movie takes place in the 1940's.
When the horse is frightened by trash collectors, it is seen to run down a lane. There is a red sports car parked at the end. The car is an MG model TD, which was put into production either late in 1951, or early 1952. It looks period, but isn't.
When Alec is being rescued in the lifeboat and calls the horse, he first shouts "Black!" with his mouth moving accordingly, then "Come on!" without any articulation.
Though Kelly Reno was an accomplished rider and did most of his own stunts, he wasn't strong enough to control the thoroughbred racehorse playing The Black in the match race scene, and there is a fairly obvious larger stunt double in a couple of shots.
When Henry and Alec take the Black to the racetrack for the first time, palm trees can be seen in the distance even though the scene is set in New York.
(at around 1h 35 mins) When Henry Dailey (Mickey Rooney) enters Alec's home and has a discussion with Alec's mother (Teri Garr), the boom mic is visible in the mirror over the fireplace.