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?
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?
Plot hole: Sarah is transmatted down to Voga after being injected with alien poison by a Cybermat. According to the Doctor, the transmat will recognise Sarah's human molecules and separate and reject the (non-human) poison molecules. As clothing fabrics tend to made of non-human molecules, how come Sarah and Harry didn't arrive on Voga stark naked?