Continuity mistake: In episodes 2 and 3, watch the clock on the wall in the Master's quarters. When the Master pulls a gun on the Doctor and the Doctor quickly pulls the door shut, the clock shows ten minutes to three. In the next episode, after the swordfight is over and the Doctor is being led out by the guards, the clock now shows approximately eight minutes after twelve.
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.