Deliberate mistake: In episode 3 of 'The Web Planet' (titled 'Escape To Danger') watch as one of the Zarbi operators, his vision impaired by the costume, runs right into the camera. So far behind schedule was the recording of this episode, however, that this mistake was retained in the finished episode, as there was no time left for a re-take.
Other mistake: Near the end of episode 5, Stevens is reading out previous numbers of slave units and B.O.S.S is telling him the new ones. For New York, the previous figure was 7203 and the new figure 7580. However, for Moscow the previous figure was 10003 (ten thousand and three), and the new figure is 110098 (one hundred and ten thousand and ninety-eight), which is a big difference.
Continuity mistake: In episode 2, when the Russian soldier is enticed into the water by the now-Haemovores Jean and Phyllis, watch his helmet, which he drops into the water as he moves towards them. When the camera angle changes to a shot of him from the front, we see his helmet slowly drift from directly behind him out to the right of screen. Then we cut to a shot of Jean and Phyllis, then back to the soldier whereupon his helmet again drifts from directly behind him off to the right. Finally, when the other Haemovores drag him down into the water, look behind him and you'll see the helmet, sitting on the beach well above the waterline...
Factual error: The Doctor mentions at one point in the story that he had once been fishing in the River Fleet with the Venerable Bede. The Venerable Bede was a distinguished 7th century scholar, who lived his entire life at Jarrow, on Tyneside, and never at any time came to London.