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.
Continuity mistake: At the beginning of the episode, the police are chasing the bus and they give the numberplate as "Whiskey nine four seven Golf Hotel Mike." That is W947 GHM, but later on when the flying bus comes through the rift in time/space, the numberplate is completely different. This is because whilst filming in Dubai, the original bus broke down and had to be replaced. (00:17:58)
Continuity mistake: On the alien ship, when the Doctor is told the bad news about the bus, his hand with the phone drops to below chest level. Then it's suddenly at chin level. (00:32:30)
Continuity mistake: When the Doctor finds the stolen cup inside Christina's knapsack, he's shown reaching for it twice, in the wide shot and the close-up. (00:38:40)
Continuity mistake: When the Doctor leans on the railing above the glacier while telling Adelaide about the Ice Warriors, he rests his left hand a ways out on the railing, in a spot where it should be visible but isn't in the next shot from behind him. (00:28:57)
Continuity mistake: When Gadget is driven to the TARDIS so the Doctor can retrieve it, the landscape around it is much flatter and without the large boulders strewn around the TARDIS when the Doctor arrived on Mars at the beginning. (00:52:41)
Continuity mistake: After Lucy gets the bottle from the guard, as she explains to the Master that her family had contacts to create something to counteract the "potions of life" used to resurrect him, she starts to take the cork out of the bottle with her left hand, the camera cuts away to the Master and when it cuts back to Lucy, her left hand is on the bottom of the bottle, before she starts to take the cork out again. (00:15:00)
Continuity mistake: After the Doctor and Wilf get off the seniors' bus, they're waving goodbye. In a close-up shot, the Doctor is waving with his right hand, but in a wider shot immediately afterwards, he's switched to his left hand. (00:25:10)
Continuity mistake: During the Doctor and the Master's conversation in the junkyard, the Master gets dust on the legs of his jeans. Just before he lightning-jumps away, the dust vanishes. (00:35:15)
Factual error: When the Immortality Gate is activated, there's a wide shot of Earth as the wave from the device goes around the planet. In another instance of a mistake made by a few previous Christmas specials, despite this taking place on Christmas Day, the North Pole is looking very, very sunny for what's supposed to be the dead of winter. (00:54:50)
Continuity mistake: After the Master changes all humans into copies of himself and Wilf says, "What have you done, you monster!?", it goes to all the different Masters in the room saying, "Are you talking to me?" The Abigail Naismith-Master is shorter than the Joshua Naismith-Master. In another shot they are the same height. The Abigail Naismith-Master is wearing very high heels and should be taller than the other Masters. (00:56:00 - 00:56:50)
Factual error: When the shot zooms out from Earth across the Solar System before revealing the narrator, Jupiter and Saturn are shown. Although scaling is somewhat exaggerated, Saturn appears to be closer to the Sun than Jupiter, which it most definitely is not in real life. (00:57:57)
Revealing mistake: Adams, the female Vinvocci, has a tendency to wrinkle her forehead, which makes the fact that her spiky head is a cap the actress is wearing very obvious.
The End of Time: Part Two - S4-E18
Continuity mistake: When Donna, on the phone with Wilf, is surrounded by Master duplicates in the alley behind her house, she has her phone to her ear, but there's a shot where she looks behind her to see two Masters, one of whom is wearing a bowtie, entering the alley, her phone is missing, only to be back by her ear in the next shot. (00:07:05)
The End of Time: Part Two - S4-E18
Other mistake: Shortly after everyone arrives on the Vinvocci ship, when the Vinvocci and the Doctor run through the door on their way to the flight deck, the Doctor comes back to get Wilf, who didn't initially follow because he was mesmerized by the sight of the Earth from orbit. It's obvious that David Tennant went just behind the door and paused briefly before coming back into the room, which is not what the Doctor is supposed to be doing. (00:16:00)
The End of Time: Part Two - S4-E18
Continuity mistake: When Wilf looks down while holding his service revolver at the end of his conversation with the Woman in White, the position of his right index finger changes between shots. (00:23:35)
The End of Time: Part Two - S4-E18
Continuity mistake: When Wilf takes out his revolver and offers it to the Doctor, he's holding it with the grip pointed toward the Doctor. In a wide shot shortly afterwards, Wilf's arm is moving to hold the gun out again, this time with the barrel closer to the Doctor. In the next shot, a close-up of Wilf, the gun is back to its first orientation. (00:25:20)
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.