The Christmas Invasion - S2-E2
Revealing mistake: After the Christmas tree has cut through the wall in the Tylers' flat, you can see marker pen where the shape has been drawn and cut out. (00:10:30)
Revealing mistake: At the end when Sarah Jane is walking towards the TARDIS and the Doctor opens the doors, the inside of the TARDIS is obviously a painting. (00:39:00)
Factual error: When Rose gets the message there are two things wrong with what you see on the phones screen: firstly on the top right of the screen you can see the icon for mute even though you heard the beep, and secondly that screen is for when you type in the number you want to call (text), not the screen for receiving a text.
Factual error: The Police motorcycle in front of the Olympic runner is an S registration, meaning it was registered in 1998. The episode is set in 2012, and there is no way the Police would have such an old vehicle on active duty.
Continuity mistake: When the two Cybermen meet the Dalek for the first time, they are exterminated. They fall directly in front of the Dalek, but when the camera angle changes to show the second Cyberman hitting the floor side on, you can see the Dalek in the background. The Cybermen both fell straight forward, so it shouldn't have been possible to see the Dalek when seeing the Cyberman side on in the next shot, as the Dalek is facing them both directly.
Continuity mistake: When the Cyberman is hit by the electromagnetic bomb, it falls to its knees, then backwards. Yet in the next shot, it is flat on its back, with its leg extended. (00:25:20)
Continuity mistake: When the Doctor first gets on his scooter, we see Rose putting her helmet on before she gets on, but she doesn't do her chin strap up. When we next see her, on the bike, her strap is done up.
Deliberate mistake: When the Doctor is watching news broadcasts from around the world about the ghosts, the newspeople from France, India and Japan should be heard speaking English because of the TARDIS' automatic translation. (00:05:55)
Character mistake: In an early scene with Yvonne Hartman, she says "We've just measured the ghosts' energy at 5000 gigawatts." There are at least two mistakes here: (1) watts are a unit of power, not of energy (that would be joules); (2) later on, when Hartman is showing the Magnaclamp to the Doctor, she refers to imperial tons and says "Torchwood refuses to go metric", but a gigawatt is a metric unit.
The Christmas Invasion - S2-E2
Revealing mistake: In the scene after the Christmas tree has been destroyed in the flat and the Doctor, Rose, Jackie and Mickey are standing outside, the robot Santas do not have any gloves on, showing human hands. (00:11:05)
Revealing mistake: When the Doctor calls Rose when she is with the Daleks, you can see on the screen of her phone that the call has been going on for at least 57 seconds, but she just answered the call. (00:06:50)
Rise of the Cybermen (1) - S2-E8
Continuity mistake: When Rose is sitting on a bench and she gets a news report on her phone, look at the top of the phone screen - it says the time is 11:35. However, several minutes later, when the Doctor and Mickey find Rose, the clock says it's only 11:36. (00:15:05)
The Christmas Invasion - S2-E2
Continuity mistake: When Danny is killed he is reduced to a skeleton but when his 'corpse' is seen on the ground only a few bones and his skull are visible.This however is impossible as a full skeleton should be seen.
Continuity mistake: When Yvonne Hartman is showing the Doctor through Torchwood after leaving the TARDIS, she goes to push a door open into the main building with one hand, but when the camera cuts to them entering the building she pushes them open with two hands. (00:20:10)
The Impossible Planet (1) - S2-E11
Other mistake: When the Doctor asks what the planet is called, Ida says, 'Don't be stupid, it hasn't got a name, how could it have a name?' A few minutes later, she tells the Doctor the planet is called 'Krop Tor'.
Character mistake: Dr Singh refers to "a single protozoa." "Protozoa" is the plural form. He ought to have said "a single protozoan." (00:08:05)
Character mistake: The Doctor gets excited about the major events of 1953 and mentions that everything was "off the ration" (that is, the food rationing put in place in the UK during the Second World War had ended). Rationing actually ended the following year. (00:05:55)
Factual error: The Koh-i-Noor, as depicted in this episode, looks absolutely nothing like the real diamond. The episode's gemstone is about the size of the palm of the Doctor's hand, and shaped in a stereotypical brilliant cut. The real Koh-i-Noor is much smaller and oval-shaped.
Continuity mistake: When Yvonne is taking the Doctor and Jackie to the Sphere Room, there is a sign opposite the door that has the words "Torchwood Institute". In the next shot where you can see the corridor from inside the Sphere Chamber, the sign has disappeared. It reappears again when Rose is going into the Sphere Chamber, but this time it has directions to the Reception, Canteen and Lever Room as well as "Torchwood Institute". It also disappears again when you see the corridor from inside the Chamber. (00:23:30 - 00:31:45)
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.