In the scene where the town meets to hear a man give a speech on Colorado statehood, you can see several people holding flags. These flags are modern day flags. Colorado was the 38th state. The US flag from 1867-1877 had 37 stars.
Dr. Quinn is evaluating Preston's condition. She discusses it with Sully. She finishes her chat with "He is quite a fighter. " This is an inside joke. Preston boxed with some men and tried to pick a fight with Sully throughout the journey to rescue the boy.
Dr Mike gives the Reverend some Dover's Powder for his tonsils. Dover's Powder was a powdered opium and ipecac in use from 1801 to 1960.