Continuity mistake: Near the end of episode 4 of "The Curse of Fenric", when Ace and the Doctor run out of the exploding bunker, the Doctor stumbles in the mud and puts his hand out to stop himself falling, getting mud all over it. The Doctor even stops to look at his muddied hand, in an almost symbolic gesture. Then the director goes in for the close-ups with the Doctor and Ace, and when the Doctor puts his hand up to rub Ace's nose (same hand), it's perfectly clean.
Continuity mistake: In episode 3, after the Nitro-9 explosion which Ace uses to blow up the wall, sealing up the mine shaft, the wall is can be seen still standing, unaffected by the blast. However, after a quick cutaway to the Doctor and Ace, the wall has vanished completely by the next shot.
Continuity mistake: In episode 2, when the Russian soldier is enticed into the water by the now-Haemovores Jean and Phyllis, watch his helmet, which he drops into the water as he moves towards them. When the camera angle changes to a shot of him from the front, we see his helmet slowly drift from directly behind him out to the right of screen. Then we cut to a shot of Jean and Phyllis, then back to the soldier - whereupon his helmet again drifts from directly behind him off to the right. Finally, when the other Haemovores drag him down into the water, look behind him and you'll see the helmet, sitting on the beach well above the waterline...
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 ★