Continuity mistake: Just before Penny Carter tells the Doctor and Donna that she's going to report them for "madness", the Doctor is seen holding Miss Foster's sonic pen, which he threw in the trash just moments earlier. (00:42:10)
Continuity mistake: The registration of Milo and Cheen's car is shown on the computer screen and stated aloud as "4-6-5-◊-6." However, there is a shot of Martha and Cheen looking out the window where the car's registration sticker is visible, showing a different registration: "9-9-6-γ-1." (00:13:15)
Continuity mistake: When the Sphere Chamber is first shown, there is a rolling staircase set up just below the Sphere. Rajesh Singh is shown climbing the staircase and nearly touching the Sphere. However, when the room is next seen, when Raj hears that the Doctor is coming and walks up to look at the Sphere again, the staircase has vanished. Later, when the Doctor and Jackie are shown into the room while Yvonne gives them the Torchwood tour, the staircase is still missing, and it's more obvious that it is no longer in the room. It does not reappear for the remainder of the two-parter.
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)
Continuity mistake: During the scene on the hospital roof, when the Doctor is telling off the Atraxi while simultaneously choosing a tie out of several he stole from the locker room, the number of ties draped around his shoulders and the position of his hands changes between shots. (00:52:35)
Continuity mistake: When the Doctor sonics the payphone so Donna can call her mother, he's doing it with his right arm, then it cuts to close-up and he's using his left arm. (00:09:00)
Rise of the Cybermen (1) - S2-E8
Continuity mistake: In this episode's TARDIS scenes, the yellow padded seat is positioned so that it's on the side of the console closer to the door, so people sitting on it are facing away from the door. In all other episodes featuring this version of the console room, the seat is positioned on the side of the console opposite the door.
Continuity mistake: Partway through the episode, there's a wide shot of London, with an undamaged Big Ben visible. The inciting incident of the previous episode was a spaceship crashing into the clock tower, severely damaging it. (00:25:40)
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: The opening shot of the episode reuses the zoom-in from orbit originally used in "Rose." The North Pole is sunlit, as it would be at the height of summer. "The Runaway Bride" takes place on Christmas Eve, four days after the Northern Hemisphere's Winter Solstice, when the Pole would be facing away from the Sun, in darkness. In fact, this was the second Christmas special in a row to make this mistake, after "The Christmas Invasion." (00:00:05)
The Christmas Invasion - S2-E2
Continuity mistake: When the robotic Christmas tree attacks Rose, Jackie and Mickey in the Tylers' flat, it barrels through the internal window and destroys a supporting pillar separating the living room from the main hallway. Later in the episode, the pillar is seen intact. (00:13:30)
The Sontaran Stratagem (1) - S4-E4
Continuity mistake: When Ross makes his "round the bend" pun while turning the Jeep onto Rattigan Academy's drive, the road seen doesn't match up with what's shown on the GPS display. (00:26:20)
The Unicorn and the Wasp - S4-E7
Continuity mistake: When Agatha shows the Unicorn's case of tools to everyone when they're all gathered in the parlour, the case is shown open just before she's shown opening it. (00:29:50)
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 end of the hospital roof scene, as the Atraxi are flying away, the Doctor is seen reacting to the TARDIS key in his jacket pocket heating up twice. (00:54:20)
Factual error: The Doctor says that the Earth is six billion years old, which is one and a half billion years over - it's only 4.5 billion years old. (00:21:25)
Audio problem: When Martha says "We're on the Moon. We're on the bloody Moon," her reflection is visible in the window in front of her. Her lips don't move. (00:07:35)
Continuity mistake: In the sphere room the Doctor briefs Yvonne and Rajesh on the void. As he sits down in front of them you see Jackie's feet start walking towards them but the next cut behind Yvonne and Rajesh facing the Doctor shows Jackie isn't there. (00:25:15)
Continuity mistake: When the Shade leaves Clara and she falls, her body is twisted because of the way her legs are bent with one on top of the other and her arms are out to the side. In the overhead shot of her, her positioning has changed, her body isn't twisted and her arms are more straight down her side.
Visible crew/equipment: When Amy is guesstimating Amelia's age, the camera pans to the right and into a crew member's arm. (00:13:49)
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.