The Christmas Invasion - S2-E2
Factual error: When the Doctor regrows his hand during the swordfight, he says that he can do this because he's still within the first 15 hours of his regeneration cycle, and there's still residual energy in his body. However: In both this scene, and the episode's opening scene, when the TARDIS arrives in London, it is full daylight. The episode takes place on Christmas Eve and Christmas Day, 3-4 days after the Winter Solstice. London, at 51°N latitude, has a night longer than 15 hours at that time of year, meaning the Doctor should have been out of luck.
The Christmas Invasion - S2-E2
Audio problem: When the Doctor is proving his identity to Harriet Jones by telling her about when they were trapped together at Downing Street, his words don't match the movements of his jaw when we see him from behind - the timing's all off. (00:40:55)
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)
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)
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.
The Christmas Invasion - S2-E2
Continuity mistake: After the Doctor's challenged the Sycorax leader to a swordfight, when he's asking about the rules of combat while taking his dressing gown (bathrobe) off, he starts taking it off beginning with his left arm in two successive shots. (00:43:58)
The Christmas Invasion - S2-E2
Character mistake: When Llewellyn is describing what was carried onboard Guinevere One, the UNIT computer displays the space probe's name misspelled "Guinivere" One. (00:26:50)
The Christmas Invasion - S2-E2
Continuity mistake: When the TARDIS crash-lands at the beginning, it comes to a halt in a corner of the Powell Estate's courtyard, by the garbage containers. Later, when Rose is watching through the window as blood-controlled people walk through the courtyard, the TARDIS has moved further out into the plaza. (00:23:05)
The Christmas Invasion - S2-E2
Continuity mistake: At the beginning of Rose and Jackie's conversation in the kitchen about the Doctor, Rose takes a piece of food out of the fridge. Moments later, when she rests her hand on the light switch by the door, it has vanished. At no point in the intervening time did she come anywhere near a spot where she could have put it down, and she didn't eat it either. (00:04:10)
The Christmas Invasion - S2-E2
Continuity mistake: When Mickey is explaining what pilotfish are, after looking it up on his computer, in most of the shots he's gesturing with his left hand, but there's one shot where he's using his right hand. (00:14:10)
The Christmas Invasion - S2-E2
Continuity mistake: When Daniel Llewellyn meets Harriet Jones, she pulls out her ID card when she introduces herself. The scene cuts to a shot of Llewellyn saying that he knows who she is, and when it cuts back to Harriet, the ID card has vanished without her making any movement to put it away. (00:16:10)
The Christmas Invasion - S2-E2
Continuity mistake: When Rose goes to look at the Doctor in bed while Harriet is speaking on TV, the bedding has changed from when it was previously seen. (00:28:05)
The Christmas Invasion - S2-E2
Continuity mistake: After the Sycorax ship has arrived above London, when Rose has decided that they need to shelter in the TARDIS and is explaining this while preparing to put a housecoat/dressing gown/bathrobe on the unconscious Doctor, the garment jumps between the bed and her hands in a few shots. (00:30:25)
The Christmas Invasion - S2-E2
Factual error: The episode kicks off with a reuse of the zoom-in from orbit first seen in "Rose." As the sunny North Pole indicates, the Earth is depicted as if it is the height of Northern Hemisphere summer, even though as the title of the episode indicates, it begins on Christmas Eve, three days after the northern Winter Solstice when the Pole is in darkness. (00:00:05)
The Christmas Invasion - S2-E2
Revealing mistake: When Daniel Llewellyn is looking up U.N.I.T. staff records on the computer, at one point a control panel for a DVD playing program is visible onscreen, showing that the special U.N.I.T. user interface is a video. (00:26:25)
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 Christmas Invasion - S2-E2
Other mistake: When Rose and Mickey are running across the plaza after being dropped off by a cab, a fence is visible between where they are and where the cab pulled up. It is unlikely to say the least that they would have gotten out of their cab right by a fence and climbed over it. (00:08:45)
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.