There are always exactly two golf balls by Ray's feet, no matter how many he putts under the dog.
Throughout the series there is a change in the character "Shamsky II". The color of the dogs are different so, it is obvious they used different dogs.
When Robert claims he knows what happened to his childhood dog, some lint on his sleeve disappears between shots.
When Robert is walking out after playing with the dog, you can see the background scenery in the far left of the screen.
When Robert learns the owner has come back for the dog, he says "Give him to her." even though he had no way of knowing that the owner was a woman.