Factual error: There are currently well over 700 different native Australian languages, and undoubtedly many more have been extinct for centuries. The chances of a 20th Century European-Australian such as Tegan being able to understand a native Australian language from around 35,000 years ago are so astronomical it is beyond belief.
Other mistake: In episode 4, as the Doctor, Tegan and Nyssa are being led away from the bridge, the Cyberleader loses his footing when he gets to the bottom step, and stumbles/trips up (He recovers himself very quickly; so quickly in fact, that this mistake was left in the finished episode). (01:24:45)
Factual error: As the spaceship approaches the Earth of 65 million years ago, the Earth looks very much like the present day one. Hasn't anyone heard of "continental drift"? The Earth's land masses of 65 million years ago were not where they are now. (This has been fixed on the DVD)
Plot hole: The freighter traveling back in time makes no sense. According to Adric, the Cybermen's computer is responsible, yet the Cybermen possess no such technology; their machine's task was simply to navigate the freighter towards Earth. The idea that time travel could happen by accident is also absurd. (01:30:05)
Continuity mistake: The mouth panel of the Cybermen costumes was originally intended to be a clear perspex panel. During filming, it was felt that this showed too much of the actor inside the Cyberman costumes. So a decision was taking - mid way though filming - to paint over the 'clear' panel with silver paint. However, this does result in the mouth panels of every Cyberman alternating from 'clear' to 'silver' from shot to shot.
Revealing mistake: During the "cliffhanger ending" at the end of episode 3, it's blatantly obvious that the three columns of advancing Cybermen are merely mirror images of each other. The head of each column has black head bars indicating leadership, and is holding his gun in exactly the same position.