Continuity mistake: In the first minute of episode three, one of the evil robot mummies attacks Sarah Jane Smith. In doing so, it lunges forward, misses Sarah Jane, and smashes the "Marconiscope" device, which explodes in flames. However, seconds later, the 'Marconiscope' device is still visible in the next shot, but totally undamaged.
Factual error: The Master states that Earth and its entire constellation were moved, but constellations are merely patterns of stars (as viewed from a given point, like Earth) that may be nowhere near each other - the Earth could not really be described as being in a constellation as any sort of specific entity that could be moved.
Continuity mistake: The Doctor can be seen wearing glasses in some long shots of him riding a motor bike. Normally, Sylvester McCoy (who played the Doctor at this time) removed his glasses before filming. Seems as though he either forgot, or could not ride a motorbike without them.
Plot hole: The temperature of the air being blown into the mines is controlled from the communications room when the Doctor needs to knock out the Ice Warriors. But conveniently, the ventilation system is controlled from the refinery when Eckersley needs to suffocate the miners.