Factual error: One of the characters in this story is called "Lord Ravensworth." Yet the story is set in 1813, and Sir Henry Liddell was not ennobled and raised to the Peerage to become Lord Ravensworth until 1821 (eight years later).
Continuity mistake: The amount of dirt on the Doctor's face changes between the Bath House and the exterior filming.
Plot hole: Peri goes to a fair bit of trouble to bolt the door on the bath house when rescuing the Doctor. When the Rani and the Master arrive, they simply open the door. Now this, in itself, isn't a mistake, as the Master has a special gadget for opening locked/bolted doors, but both the Master and the Rani seem surprised that someone is in the bath house.
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★