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 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)
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 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)
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)
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 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)
The Family of Blood (2) - S3-E9
Continuity mistake: When the Doctor comes back to the Cartwright house after imprisoning the Family, Joan walks over to the window and looks out, clasping her hands in front of her. In the next shot, when she asks the Doctor if it's done, her hands are suddenly by her sides, and she is shown clasping them again. (00:34:45)
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)
The Family of Blood (2) - S3-E9
Continuity mistake: When Martha finishes listing off the bones of the hand to Joan, in order to prove that she's a medical student from the future, in a shot facing Joan, Martha's thumb is extended. In the next shot, facing Martha, her thumb is suddenly folded back, as if she was using her hand to display the number 4. (00:12:15)
The Family of Blood (2) - S3-E9
Continuity mistake: When Sister of Mine enters the school's courtyard after the battle with the scarecrows, her right hand is holding her balloon at the bottom, with the bottom of the string wrapped around her left hand. In the next shot, facing her, her right hand is at her side, with the balloon floating above her left hand. The balloon proceeds to jump between positions until Sister of Mine murders the headmaster. (00:18:00)
Continuity mistake: At the beginning, when the Doctor asks Martha if they saw her face, her hands change position, from grabbing his arms in a shot facing her to facing up in a shot with both of them. (00:00:10)
Continuity mistake: When the Doctor says, in response to Martha asking how the Family can follow them, "Stolen technology. They've got a Time Agent's vortex manipulator," in a close-up of his face he reaches with his left hand for a control on the console, but in a following shot of his hands, they're right next to each other. (00:00:25)
Continuity mistake: When Martha and Jenny are washing the floor, just as Hutchinson and Baines come along and tell them off for laughing, one of the lace ribbons on Martha's cap moves between hanging in the back in shots facing her and draped over her shoulder in shots facing the schoolboys. (00:04:15)
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.