Other mistake: When the K1 Robot breaks out of Kettlewells factory in part 2 or 3, it trips up.
Revenge of the Cybermen - S12-E5
Other mistake: Shortly after the Doctor makes his speech to the Cybermen about how pathetic they are, you can see a Cyberman's head wobble.
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 ★