Elizabeth Quinn is surprised that Sully is so well versed in ancient proverbs. This does not make sense. He simply repeated what she said first: When in Rome do as the Romans do.
The US flag at the train station has too many stars.
In some scenes Dr Mike is wearing frosted lipstick which was not invented until the 1920s.
Matthew, barely 17 years old, offers Sully, a widower, guidance on wooing a woman. This is not realistic.
Elizabeth Quinn describes Dr. Quinn "a mature woman." This is ironic. Dr. Quinn has stunted emotional growth. Sully is younger, but more in touch with his emotions.