When Toberman throws the cyber controller it's obviously a dummy as the head comes off and is back in position in the next shot when it's apparently dead.
When the Cybermen enter their hibernation pods, the footage is just played backwards from when they exited them in part 2. As a result, the plastic sheeting that covers the pods magically heals itself from where it was torn previously.
When the Cyber Controller shoots Kaftan, the projectile from the prop gun flies off to her left, clearly missing her. Nevertheless, smoke billows from her body and she falls dead.
In part 2, the rocket captain informed the crew that repairs to the rocket's fuel system would take at least 72 hours, necessitating them spending the night in the tomb. Here, he announces that repairs have been complete. Less than 24 hours have passed in story time.
The shadow of a boom microphone moves across Jamie's face in the opening scene.
After he follows the cyberman controller out of the tomb, a boom microphone shadow can be seen next to the Doctor's shoulder.