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 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?
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.
Continuity mistake: As Jo walks along the castle ledge to escape from The Ice Warriors' room, there is, at one point, a quick shot of a piece of the ledge breaking off under Jo's shoe and falling down the cliff face. However, the shoe isn't Jo's. If you look closely, you'll see that the shoe in that brief shot is more pointed and of a darker colour than the shoes Jo is wearing, and has a strap across the ankle instead of being a slip-on.