The Family of Blood (2) - S3-E9
Continuity mistake: When the Doctor and Martha hug after he thanks her for looking after him, the position of her arms changes between shots. (00:38:20)
Continuity mistake: When Sally pulls off the last piece of wallpaper to reveal the writing, "Love from the Doctor (1969)", in the first shot, the second "9" in the date is somewhat patchy, with the middle part of the number mostly gone due to the removal of the wallpaper. In a close-up of "The Doctor" just moments later, the "9" is intact, visible in the lower right corner. (00:02:15)
Continuity mistake: When Sally Sparrow is about to take the key from the weeping angel, at first the key is on a piece of string, and that string is wrapped around the weeping angel's left hand. In the next shot, and when she pulls the key out, the string is now only in the angel's palm. (00:10:30 - 00:11:10)
Continuity mistake: When Sally enters the DVD store looking for Larry, she encounters the store's owner, Banto, who is sitting behind the front counter watching a movie. He holds up his finger to indicate her to wait briefly because of the point in the movie he's at. In shots facing him, his hand is quite close to his mouth and chin, but in a shot facing Sally, his hand is considerably further away from his head. (00:13:10)
Continuity mistake: When Sally picks up the remote to pause the recording of the Doctor after getting unnerved by him seeming to hear her, and when she rests it against her forehead after Larry comes back into the room, it switches between her hands a few times. (00:16:40)
Continuity mistake: After Sally leaves the garage, Billy turns his head and sees the Weeping Angels around the TARDIS, and his facial expression changes from a smile to a confused frown. In a close-up of Billy after the shot of the Angels, his head is turning and his expression changes a second time. (00:20:40)
Continuity mistake: When Sally is holding the picture of Billy and his wife, the position of her right index finger on the frame changes between shots. (00:24:35)
Continuity mistake: When Sally takes out the list of DVDs while talking to Billy in the hospital, her grip on the paper changes between shots. (00:25:40)
Continuity mistake: When Lawrence is watching the Weeping Angel, just after seeing the Doctor's film/Easter egg, he turns away for a split second. By the time he turns back, you see the Weeping Angel's face only inches from Lawrence's face. But you then cut to a wide shot where you see the Angel's arms outstretched, so its face is about half a metre away from Lawrence's face. (00:34:45)
Continuity mistake: When Sally and Larry are hugging each other as the TARDIS dematerializes around them, as the cellar with the Angels becomes more visible, Sally lets go of the console with both hands and clasps them together. A couple of shots later, her left hand is still touching the console. (00:37:55)
Utopia (1) - S3-E11
Continuity mistake: When everyone is being escorted into the silo after escaping the Futurekind, they all have mud splattered on their clothes - it's especially noticeable with the Doctor, Padra and Jack. Inside the silo, the mud has disappeared. (00:12:20)
Utopia (1) - S3-E11
Continuity mistake: When the Doctor gets the rocket to work by tinkering with the boost reversal circuit, he picks it up with his left hand, sonics it, and then transfers it to his right hand, all in a shot where he has his back to the camera. In the next shot, facing him, he's holding it in his left hand as he pulls something off the device. The shot after that, facing Professor Yana again, the circuit is back in his right hand. (00:18:50)
Utopia (1) - S3-E11
Continuity mistake: When the Master takes the disc with the location of Utopia out of the computer, the exact spot he's holding it changes between shots. (00:40:55)
The Sound of Drums (2) - S3-E12
Continuity mistake: When the Doctor fixes Jack's vortex manipulator so they can escape the silo, Martha and Jack are holding the lab door mostly closed against a horde of Futurekind. In the shot where the trio time-travels away, the Futurekind, some of whom had stuck their hands through the gap in the door, are missing. (00:00:40)
The Sound of Drums (2) - S3-E12
Continuity mistake: At the beginning of the Cabinet meeting, when the Master says, "Thank you. Thank you, one and all," in a wide shot, he turns his head to his right. In a close-up immediately afterwards, his head is facing straight ahead. (00:04:00)
The Sound of Drums (2) - S3-E12
Continuity mistake: During the Cabinet meeting, when the Master stands up as he says, "That wasn't funny," in a shot from behind he places both hands on the table as he rises. In the next shot, facing him, his right hand is suddenly by his chin. (00:04:10)
The Sound of Drums (2) - S3-E12
Continuity mistake: When gassing the cabinet members, the Master puts on a gas mask. The Valiant logo is above the tube, and upside down. In the next shot, it is below the tube, and the right way up. (00:04:50)
The Sound of Drums (2) - S3-E12
Continuity mistake: When the Doctor talks about how the Master was always sort of hypnotic, in a wide shot, Martha is sitting on the end of her couch, with her hands loosely folded, with her left hand on top. In the shot of her where she says she was going to vote for Harold Saxon, her right hand is on top. In the next wide shot, her hands have reverted to their original position. (00:12:05)
The Sound of Drums (2) - S3-E12
Continuity mistake: When Martha starts to phone her family, after the Doctor warns her not to tell them anything, as she snaps in response, "I'll do what I like!", in the first shot she's holding her phone away from her body, but in the second shot it's jumped to her ear. (00:14:25)
The Sound of Drums (2) - S3-E12
Continuity mistake: When Jack tells Martha they have to ditch her car after escaping from the Master's thugs, the position of her hands on the steering wheel changes between shots. (00:17:05)
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.