Sully reveals that he is afraid to ride a horse because he watched his brother die by being dragged by a horse. In a later episode, Sully reveals that his father died before he knew him and that his mother died when he was 10 years old. He lived in New York City. He said he moved alone to Colorado at that time. That story line does not align with his brother ever existing.
Ethan Cooper offers to carry Dr Mike's parcel from the telegraph office. As they walk past the clinic door Ethan still has the parcel. When they reach the barber shop Ethan is no longer carrying the parcel.
Near the 16 min mark, Matthew is seen wearing pants with belt loops. Belt loops weren't invented until 1922.
After the Harriet dies of a burst appendix, Ethan consoles Dr. Quinn. He says that Harriet told Dr. Quinn that she had eaten some bad peaches. Ethan was not present in the room when the woman and her children were getting vaccinated. Ethan had not even revealed his true identity yet. Ethan would not had known about the bad peaches.
Sully bought a horse from Ethan. Sully learned to ride the horse bareback. Sully road the horse to town for the party / festival. Suddenly Ethan whistles and the horse breaks free from the hitching post. The horse is wearing a saddle. There is no logical explanation for the horse to be wearing the gear.
Dr. Quinn is chaste. She is a proper professional woman from a well to do family of Boston. The neckline of her party dress is too low for her moral and professional standing.
Dr. Quinn is driving the wagon with Matthew sitting beside her. She typically allows a man to drive.
Dr. Quinn sews Ethan's wounds in the barbershop. She typically has her patients moved into the Clinic.
Dr. Quinn does not insist on examining Harriet when she was at the homestead. Typically Dr. Quinn demands on examining a person who exhibits signs of illness.