Revealing mistake: In order to save money filming the lift-off of Crayford's rocket from Oseidon, the producers decided to use stock footage of a Saturn 5 blast-off. Unfortunately, that meant the words "UNITED STATES" in large red lettering are seen on the side of the rocket...which is a little bit of a giveaway, especially as the rocket is supposed to be a BRITISH space probe.
Visible crew/equipment: In episode one, the Doctor and Sarah crouch behind a pod to escape the android laser fire. They lie on a large brown piece of cloth conveniently placed to keep them from getting dirty.
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 ★