Remembrance of the Daleks - S25-E1
Factual error: The events depicted are supposed to have taken place at the time of the broadcast of the first Doctor Who story... Saturday 23rd November 1963 at 5:15pm. However, the non-wintry weather and the bright evenings don't fit late November/early December.
Factual error: In 1638, a mathematician calculates that the asteroid will return in 350 years time, on the 23rd of November 1988. But in 1752, Britain's calendar was moved forward 11 days so that it matched with that of the Vatican. This means the asteroid would return on 4th December, so everything that is supposed to happen in this story after 1752 is 11 days out.
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 ★