Toward the end of the race, while Sully is supposedly off checking how Michaela is doing, suddenly we see him with Colleen and Brian cheering. Then in the next scene, there he is coming back, running up to Colleen and Brian who are alone.
When Snowbird gives Dr Quinn a horse, Snowbird calls the horse two different names.
When Brian is rolling out his pie crust, long shots show the rolling pin completely clean, while close shots show the dough stuck to the rolling pin.
At the end of the race Flash's neck is lathered with white sweat, then when Dr Mike dismounts the sweat is gone.
Based on the white blaze on Flash's face, several different horses were ridden in the race posing as Flash.
Hank's new horse is named Hurricane. The word hurricane was coined in the 1950s.
Dr. Quinn demonstrates the tricks that Flash can perform. There is no indication that anyone showed Dr. Quinn that this horse was trained.