Continuity mistake: When the Doctor and Harry arrive in the cryogenic chamber, they walk around for some time inspecting the chamber and talking. Towards the end, they notice a green slime trail newly appeared on the floor. But the trail was visible in the very first overhead shot of the chamber.
Continuity mistake: When Sarah falls from the scaffolding, a plank of wood saves her from death. Trouble is, she fell a foot from the outside of the scaffolding and most of the plank was inside the scaffolding, therefore her feet would have hit it and she could only have landed with her head pointing inwards. But when we see her, her head is pointing outwards. (00:01:25)
Plot hole: The linchpin of the plot makes no sense whatsoever. In an effort to diffuse international tension, the superpowers would allow Britain to publish the codes that would allow anyone in the world to launch their nuclear missiles? And then, after going through the drama of not one but two countdowns, it's revealed that the superpowers can just activate safety over-rides to prevent the launch. So how in Hades did the SRS have any threat whatsoever to wield over them and issue their demands?
Revealing mistake: During the Doctor's early conversation with the Time Lord, there is fog swirling around them. When the Doctor agrees to take on the mission, it suddenly appears very concentrated around the tip of the rocks behind them, as if generated from a source behind the rocks. Normal fog would not do this, and it's clear that dry ice was used as the fog effect (DVD commentary confirms this). (00:02:45)
Revealing mistake: Whenever there's a close-up of Davros, it's very easy to see that there's a gap around his mouth where the mask should blend in with the actor's face, but doesn't. This mistake was rectified, incidentally, in Davros' next appearance in "Destiny of the Daleks."
Plot hole: The Vogans live on a planet made of gold. They helped develop the gold weapons that defeated the Cybermen. They know the Cybermen are coming and live in a state of paranoia about that eventuality. So why in the world do they attack the Cybermen with useless projectile weapons instead of "glitter guns" or some other gold-based weapon?
Continuity mistake: The use of gold against the Cybermen is wildly inconsistent in this episode. It is said that it suffocates them. Yet Cyberman have been seen functioning perfectly in vacuum ("The Moonbase" and "The Wheel in Space"), it affects the Cybermats, who are little more than metal drones, and it affects the Cybermen's radar, which does not breathe.