The untamed horse that Seth rides has a completely black forehead. The horse that Spotted Eagle 'tames' is a different one. It has a white spot on its forehead.
When Seth mounts the horse and it starts bucking, you can see that the rider is clearly a stunt man. He is taller and stockier than the actor who plays Seth.
Seth supposedly lives in Walnut Grove with his family yet this episode is the only time he is seen at school with the others.
Laura's necklace from the Osage chief was a small medicine pouch but she now calls it her bear claw. The audience is left to assume it was not stolen or lost in the pond fight scene.