Factual error: When Ms. Booth is going upstairs to the room rented to W. Turner she is holding the kerosene lamp. The scene takes place around 1829 and the kerosene lamp was invented in 1853.
Factual error: When the Doctor visits William Turner in Chelsea, he claims to be leaving by train from Charing Cross. That station did not open until 1864 - 13 years after the death of Turner.