Factual error: The Doctor postulates that ammonium sulphide will poison The Ice Warriors because the Martian atmosphere is composed mainly of nitrogen. However, it is the EARTH's atmosphere that is mainly nitrogen (78%) whereas Mars' atmosphere is 95.3% carbon dioxide.
Factual error: It is stated that removing all the plants caused carbon dioxide levels to drop. But plants absorb carbon dioxide, so removing them would create an increase.
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 ★