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?
Continuity mistake: In episode 2, 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.