The Power of the Daleks - S4-E3
Revealing mistake: The Daleks that appear in this and other Doctor Who stories were rather expensive, so some ingenuity was required to make the small number available look like they were more than they were. Tricks employed in "The Power of the Daleks" included making four Daleks look like an army by having them circle around the set a few times (note the delay between the fourth Dalek exiting and the "fifth" Dalek entering), and the blatant use of photographic blow-ups in place of "real" Daleks.
The Power of the Daleks - S4-E3
Deliberate mistake: During all the animated parts of "The Power of the Daleks" in numerous shots various illustrated character's such as The Doctor, Polly, and Ben have their buttons, pockets, patches, etc, flipped to the opposite side, sometimes even within the very same shot.
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 ★