Revenge of the Cybermen - S12-E5
Continuity mistake: The use of gold against the Cybermen is wildly inconsistent in this episode. It is said that it suffocates them. Yet Cyberman have been seen functioning perfectly in vacuum ("The Moonbase" and "The Wheel in Space"), it affects the Cybermats, who are little more than metal drones, and it affects the Cybermen's radar, which does not breathe.
Revenge of the Cybermen - S12-E5
Continuity mistake: At the end of "Genesis of the Daleks", the Doctor was wearing his big brown overcoat. However, at the beginning of this episode, he is wearing his red jacket again.
Revenge of the Cybermen - S12-E5
Continuity mistake: For a supposedly emotionless creature, the Cyberleader is easily provoked to a fit of rage, including throwing the Doctor around the Beacon.
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 ★