The Curse of Peladon: Episode One - S9-E5
Plot hole: The delegate Alpha Centauri is a 'hexapod' - a creature with six legs and feet. ('Hex' = "six", 'pod' = 'foot'.) But throughout this Doctor Who story, Centauri can be seen with all six legs and feet in the air, projecting from the front of the creature... so what is it walking around on?
The Sea Devils: Episode Four - S9-E12
Plot hole: The Doctor and the Master both surface in bright orange diving suits and are the only two wearing them. But when the supposed body of the Master is dragged out it is also wearing an orange diving suit, and the Doctor and Master are still wearing theirs, so a third suit appeared from nowhere.
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 ★