Continuity mistake: At the start of the story (the beginning of episode 1) the TARDIS materialises on its side, but at the end of the story (the end of episode 6) the TARDIS dematerialises right side up.
Plot hole: We twice see a map of how far the ice is away from the house, once in the first episode, and later in episode five. The ice has moved most of the way across the map in this time, and the distance it has moved is stated to be a 100 metres. This would place it only 20 metres from the base. The problem with the distance is that it takes Penley quite a while to get the injured Jamie to the base, including a stretch across open ground. Also, The Ice Warriors weapon targeter suggests the base is as much as two kilometres away. So just how far away is the ice; 20 metres, 2 kilometers...or somewhere in between?
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 ★