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)
Continuity mistake: When the Connollys are watching TV, in the shots facing the chair and sofa, the chair Eddie was sitting in is further away from the couch than in the shots from above, where the chair is almost touching the couch. (00:04:46)
Continuity mistake: Jackie gets Elton to take his shirt off by deliberately making a huge red wine stain on the front. When Elton comes back to the estate with the pizza, his shirt is unstained. (00:27:17)
Continuity mistake: Rita has her right arm up in front of her while her husband is shouting at her. She lowers her arm, and in the next shot, she is holding it up again. (00:10:10)
Continuity mistake: When Rose is hanging onto the lever and beginning to lose her grip, in close-ups of her face her body is facing the other wall of the room, perpendicular to the floor. In shots showing her and her hands on the lever, her body and head are facing the floor. (00:35:55)
Continuity mistake: After Pete tells the Doctor that Mickey went ahead because he wanted to find Rose, the Doctor asks him if he knows that Rose is his daughter from a parallel universe. The problem is that in Pete's last scene in "The Age of Steel", the Doctor saw Rose call Pete "Dad", leading to Pete departing in a hurry. (00:15:05)
Continuity mistake: When Jackie enters the TARDIS and closes the door, it shuts completely - despite the fact that there's a cable running out the door to the device the Doctor set up to catch one of the ghosts. (00:12:45)
Continuity mistake: When Yvonne leads the Torchwood soldiers in a round of applause for the Doctor and he starts lowering his hands, he does it twice, once in a shot facing Yvonne and again in the next shot facing him. (00:18:35)
Continuity mistake: After the scribble creature has been analyzed and found to be made of graphite, the Doctor takes out a pencil and erases some of it to confirm this. The next time the graphite ball is seen, the erased area is gone. (00:14:35)
Continuity mistake: When the Doctor takes a swipe out of a jar of jam in Trish's kitchen and sticks his finger in his mouth, he only has his index finger in his mouth. The scene cuts to Rose giving him a "WTF" look, and when it cuts back to the Doctor he suddenly has two fingers in his mouth. (00:21:15)
Continuity mistake: When Rose grabs the drawing of the Doctor and the TARDIS from Chloe, the upper right corner is bent over rather sharply. In the close-up of the picture as Rose tells the Doctor she'll find a way to get him out of there, the paper is now only slightly wrinkled. (00:30:15)
Continuity mistake: When the Isolus leaves Chloe, in the shot facing Chloe where it says goodbye, Chloe's hand is raised to the wall, where the two were drawing a picture of the Earth. In the wide shot where the Isolus leaves Chloe's mouth, her arm is lowered. In the next close-up of Chloe, when she says "Mum?", her arm is raised again. (00:36:05)
Continuity mistake: When the Doctor first appears in the episode, baiting the Hoix with a piece of raw meat, the meat turns around in his hand between the close-up and the wide shot. (00:02:30)
The Impossible Planet (1) - S2-E11
Continuity mistake: In shots of the base's Ood habitation area from above, the Ood are shown in four rows from left to right, with the Ood in the third row standing with their backs against the room's middle partition and the other rows sitting on benches. However, in a shot from inside the lower area when the Doctor and Rose first go to Ood habitation, the third row is shown sitting as well. Not until later in the episode, when Danny is ordering the Ood to remain in the room, is the third row shown standing again. (00:25:15)
The Impossible Planet (1) - S2-E11
Continuity mistake: When the underground cavern is first shown, the descent pod is at the bottom of a pile of rubble up against the wall at the bottom of the drilled shaft. However, in the shot of the cavern shown when Ida says "My god, that's beautiful," the pod and pile of rubble is further away from the wall. (00:37:00)
The Impossible Planet (1) - S2-E11
Continuity mistake: When Rose is talking to Danny about the Ood, in one shot she's holding her cup with two hands, only for her to be holding it with only one hand in the next shot. (00:11:25)
The Impossible Planet (1) - S2-E11
Continuity mistake: When Rose takes out her phone and finds there's no signal, she slides it open twice, in the wide shot and close-up. (00:23:15)
Continuity mistake: When the Doctor is in the cage with the faceless people, his flashlight switches from his left hand to his right hand and back. (00:18:25)
Continuity mistake: When Jake turns on the light in the cabinet with the Cyberman on the zeppelin's bridge, he's holding his handgun in his left hand. The scene cuts away to Mickey briefly, and when it cuts back to Jake his gun has jumped to his right hand. (00:24:30)
The Girl in the Fireplace - S2-E7
Continuity mistake: For most of the scene where he's probing Reinette's mind to find out what the clockwork droids want with her, placing his hands on her temples, the Doctor's left hand is positioned with two fingers on either side of her ear. When he realises that she's seeing some of his memories, his ring finger has jumped to being in front of her ear, without him taking his hands from her head. (00:20:50)
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.