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.
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.