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)
The Pyramid at the End of the World - S10-E8
Continuity mistake: When the Doctor, Bill, Nardole, et al. first see the pyramid their long shadows are cast directly in front of them, but when the Doctor decides to "bring it" and crosses the barrier, their long shadows are cast directly to their right. Then it keeps changing in the following shots when the Doctor approaches the pyramid. (00:10:45)
The Pyramid at the End of the World - S10-E8
Continuity mistake: When Erica's eyeglasses get smashed, they're seen in a closeup inside her bag and the lens frame is cracked, but when she takes it out of her bag both lens frames are intact around the broken lenses. Also, when Erica takes the eyeglasses out of her bag she holds the eyeglasses' right temple in the closeup, but in the next shot it's the left temple being held up. (00:06:15)
Continuity mistake: During the Doctor and Sarah Jane's conversation in the café, when Sarah says that she missed him and he responds that she was getting on with her life, in a shot facing Sarah, the Doctor's hands are not visible repairing K9. In the next shot, facing him, his left hand is suddenly on the robot, in a position where it should have been visible in the preceding shot. (00:17:45)
Continuity mistake: When Mickey pulls the blanket off K9 and turns him on to ask if he has anything to get them inside the locked school, K9's right side panel is missing, exposing the wires and circuitry inside him. When he turns up in the cafeteria to help the others escape the Krillitanes, the missing panel has suddenly appeared. (00:34:10)
Continuity mistake: When Sarah Jane breaks into the school, she has her purse with her. However, after she runs out of the hall with the headmaster's office after hearing some unsettling noises, it disappears, as she no longer has it when she finds the TARDIS hidden in a storage room off the gym.
Continuity mistake: During the Doctor and Sarah Jane's conversation in the café while he's repairing K9, when Sarah mentions the events of "The Christmas Invasion" and the Doctor confirms that he was there, the Doctor's hold on a piece of wire from K9's insides changes between shots. (00:17:20)
Continuity mistake: When Cassandra, after possessing Rose, is checking out her new body in a mirror, when she starts jiggling up and down, her right hand changes position between shots of her and shots of her reflection. (00:13:40)
Continuity mistake: When Cassandra, possessing Rose, answers her phone, as Chip is telling her that Rose's accent is "Old Earth Cockney", she puts the phone to her ear twice. (00:14:55)
Continuity mistake: When Cassandra reveals her presence to the Doctor, she starts off by turning him to face her, then pulling his tie out of his jacket with her right hand and tightening the knot with her left hand, in a shot facing him. In the next shot, facing her, she has her right hand holding the knot of the tie. Finally, just before Cassandra reveals her identity to the Doctor, shortly later, which hand is holding the tie changes again. (00:23:20)
Continuity mistake: When Cassandra, possessing Rose, confronts the Doctor after he wakes up in one of the clone pods and tells him how she intends to kill him, her hand changes position between the shot from inside the pod, when she rests her hand on the front, and the next shot from outside the pod. (00:24:20)
Continuity mistake: When the Doctor is attaching the ring device to the elevator cable, the position of his hand as he's holding it in place changes. (00:34:10)
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 Parting of the Ways (2) - S1-E13
Continuity mistake: At the beginning of the scene where Rose, Jackie and Mickey are in the restaurant, in the wide shot, Rose moves her left hand to the side of her head, while looking down with her head facing towards the other side of the table, which her elbow is resting on. In a close-up immediately afterwards, she's looking out the window with her hand to her face and her elbow resting on the windowsill. (00:18:50)
The Doctor Dances (2) - S1-E10
Continuity mistake: When the Doctor is looking at Rose's hands, turning them over repeatedly, while she's describing how she was hanging from a barrage balloon, there's one moment where her hands are turned palm-up in a shot facing her, but back-up in a shot facing him. (00:18:25)
Continuity mistake: When the Doctor meets Nancy, when she warns him not to answer the TARDIS' ringing (fake) door phone, in a shot facing her he's holding his jacket away from his chest, but in the next shot facing him that hand is empty. (00:06:55)
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.