Destiny of the Daleks - S17-E1
Factual error: Davros comments that, between them, The Daleks are carrying half a megaton of explosives - in other words, roughly twenty-five times more explosive force than the Hiroshima or Nagasaki bombs. An explosion of that size should cause enormous destruction (vaporizing everything within roughly two kilometers), yet when the Doctor detonates them they explode with about as much power as a small stick of dynamite each.
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 ★