Factual error: It is claimed that a meteor shower has been diverted towards the Wheel by a star in M13 (the Hercules Cluster) going nova. As M13 is a globular cluster in the galactic halo, some 34,000 light years away from Earth, it would have to be one almighty nova to affect the course of a meteor shower in our solar system - due to the countless gravitational forces between M13 and the plane of the Milky Way - and been caused at least 34,000 years before the time of the story.
Character mistake: The Doctor (Patrick Troughton) makes one of the funniest fluffed lines in the entire history of Doctor Who in the final episode. With all sincerity he says "We'll all be dead soon, unless you switch over to the sexual air supply." (The word Troughton was probably looking for was "sectional.").
Plot hole: When the airlock door is opening at the end of the final episode, the Cyberman is the only one who appears to be affected by the air rushing out. Although 'rushing out' is probably overstating the speed of the 'explosive decompression'. It's not so much an explosion as a gentle breeze...
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 ★