Factual error: Titan is depicted as a Moon-like landscape with no atmosphere. In actual fact, Titan has a nitrogen/argon atmosphere denser than Earth's, and a reddish-orange sky. This was detected almost thirty years before "The Invisible Enemy" was made, so somebody slipped up in doing their research.
Underworld - S15-E5
Factual error: While it's true the centre of a planet would have no net gravity, the weightless condition would be everywhere, not concentrated in a convenient shaft.
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 ★