Plot hole: When the airlock door is opening at the end of the final episode, the Cyberman is the only one who appears to be affected by the air rushing out. Although 'rushing out' is probably overstating the speed of the 'explosive decompression'. It's not so much an explosion as a gentle breeze...

Factual error: In the story "The Wheel In Space", it is claimed that a meteor shower has been diverted towards The Wheel by a star in the M13 Hercules Cluster going nova. As M13 is a galaxy some 34,000 light years away from Earth, it would have to be one almighty nova to affect the course of a meteor shower in our galaxy - due to the countless gravitational forces between M13 and the Milky Way - and been caused at least 34,000 years before the time of the story.

Other: The Doctor (Patrick Troughton) makes one the funniest fluffed lines in the entire history of Doctor Who the final episode. With all sincerity he says "We'll all be dead soon, unless you switch over to the SEXUAL air supply". (The word Troughton was probably looking for was "sectional").