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.
Factual error: When the group divide up into parties, the leaader says they need to be at the rocket at 1630, so meet here at 1625. He then goes on to say that will give them an hour to look for anyone that's missing. The other actors seem to notice his mistake because they either look puzzled or look off camera, probably seeing if anyone would shout "Cut."
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Factual error: The Doctor postulates that ammonium sulphide will poison the Ice Warriors because the Martian atmosphere is composed mainly of nitrogen. However, it is the EARTH's atmosphere that is mainly nitrogen (78%) whereas Mars' atmosphere is 95.3% carbon dioxide.