Continuity mistake: When the Doctor grabs the rope there are several metres more behind him. But, as he's hoisted off the ground, he is almost at the end. (00:03:34)
Other mistake: When Miss Hartigan is testing the earpod control, the men start off facing her. She instructs them to turn to the right. They turn 90 degrees clockwise. She then tells them to turn to the left. They turn 180 degrees anticlockwise. However, they should have only turned 90 degrees anticlockwise, and end up facing her again. What they actually do is turn on the spot, as opposed to turning left. It takes a further instruction from Miss Hartigan for them to face her again. (00:24:57)
Revealing mistake: The Cyber-Leader has a clear section in the top of its head through which its brain can be seen. The brain in question is very obviously plastic.
Factual error: During the climax, the Moon is visible in the background, and is depicted as full. On December 24, 1851 in real life, the Moon was at first quarter phase.
Chosen answer: The Master knows that deep down, he deserves death for the crimes that he's committed throughout his life, and since he regards The Doctor as his arch-foe, he expects it to be at his hands. The fact that The Doctor is still willing to forgive him for all of his crimes hurts him more deeply than death would.
Captain Defenestrator