Continuity mistake: After the Doctor gets directions to the motorway, when the red-haired female pharmacist leans over her counter to try and persuade him to buy some Happy, her hands change position between shots. (00:08:00)
Continuity mistake: When the Doctor first enters Shakespeare's room at the inn, the collar of his coat is askew. The scene cuts to Shakespeare, and when it cuts back to the Doctor his collar is now flat, without him having moved his hands from his pockets. (00:09:20)
Visible crew/equipment: After the acting Prime Minister gives orders to the sergeant and the lift doors close, the soldier turns around. As he issues orders, the boom mic is reflected on his goggles. (00:05:25)
Silence in the Library (1) - S4-E8
Continuity mistake: When the girl recognizes the Doctor on her TV, telling him that he was in her library, and he reacts, the position of her pencil crayon in her hand changes between shots. (00:20:45)
Last of the Time Lords (3) - S3-E13
Continuity mistake: When Martha explains to Tom and Professor Docherty about how the Master could only use the TARDIS to travel between the present day and the end of the universe, and how he must have gone to Utopia, in a wide shot her right hand is resting on the table, but in a shot from above looking down on the captured Toclafane her right arm is by her side. (00:20:15)
The Sound of Drums (2) - S3-E12
Continuity mistake: After the Master calls Winters "the last President of America", in a shot from behind him and Lucy, he has his hands by his sides. In the next shot, facing them, the Master has his hands clasped behind him. (00:31:35)
The Lazarus Experiment - S3-E6
Continuity mistake: After Lazarus emerges from the pod, when he announces himself to the crowd, in a wide shot, his arms are lowered, but in a close-up immediately afterwards his arms are raised. (00:09:15)
Forest of the Dead (2) - S4-E9
Continuity mistake: After the Doctor tints Anita's visor, as he explains to River that he did it to try and trick the Vashta Nerada into thinking they're already inside Anita's suit, the position of his right hand, holding the sonic screwdriver, and the fingers of that hand change position between shots. (00:10:25)
Continuity mistake: When the Doctor picks up a skull from the bones waiting to be ground into fertilizer, the position of his hands holding it changes between shots facing him and shots looking at the skull. (00:15:10)
Continuity mistake: When the Doctor starts scanning the wall of the tunnel as Jenny asks him who he is and if he's an anomaly as well, his grip on the sonic screwdriver changes between shots. (00:22:20)
Continuity mistake: When the Doctor and Donna leave as Caecilius, Metella, Evelina and Quintus stand and watch the destruction of Pompeii, the TARDIS changes orientation between shots - in both of them, one from in front of the family and one from behind, the TARDIS' door, with the sign, is visible. (00:45:10)
Continuity mistake: When the Doctor and Donna are talking to Caecilius, when they introduce themselves as "Spartacus" and Caecilius makes several guesses as to their relationship, wondering if they're married or siblings, in shots facing them, the Doctor and Donna are standing fairly close together. In shots facing Caecilius, however, the Doctor and Donna are standing much further apart. (00:11:05)
Continuity mistake: When the Doctor interrupts Mr. Copper's incredibly inaccurate description of Earth society to ask him where he got his information from, in a shot facing Mr. Copper, the Doctor's raised hand has only one finger extended. In the next shot, facing the Doctor, he has two fingers extended, with the other two only loosely curled. Shortly after this, the Doctor scratches his temple with that same hand, only for it to be absent in the next shot facing Mr. Copper. (00:11:40)
Continuity mistake: After Milo and Cheen abduct Martha, they put a sleep patch on her before entering their car. In the close-up where Cheen applies the patch, it's stuck on securely and neatly, with the top and bottom of the square pointing directly at Martha's head and chest respectively. In a wide shot immediately afterwards, the patch is stuck on quite loosely and has gone askew. (00:06:35)
Continuity mistake: When the Doctor and Martha open the doors to the balcony, in a shot facing them, Martha lets go of the handle of her door and it swings completely open. In the next shot, from behind, Martha is still holding the doorknob. (00:10:35)
Continuity mistake: When the Doctor is looking out the window while asking Martha if there's a balcony on the floor of the hospital they're on, in close-ups of him only his right hand is visible, resting on the sill between two windowpanes, and his left arm is by his side. In a wide shot from outside looking in, his left arm is stretched out with his left hand gripping the divider between two windowpanes, in a spot where it should have been visible in the preceding shot. (00:10:05)
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 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)
Continuity mistake: When the Doctor is restrained by two of the Editor's corpse minions, and the Editor demands to know who he is, the hand of the one holding the Doctor's right arm moves between his chest and shoulder several times. (00:30:50)
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.