The Unicorn and the Wasp - S4-E7
Continuity mistake: After questioning the houseguests, the Doctor and Agatha are talking. She uses the phrase "little grey cells", and the Doctor responds, "Oh, yes, little grey cells. Good old Poirot." When he does this, he's holding a saucer in his left hand and rests a teacup he's holding in his right hand atop it, as he turns toward the chair that the suspects were sitting in. In the next shot, as he walks over and sits in the chair, he is suddenly holding the teacup and saucer in his right hand, with his left hand in his pocket. (00:13:55)
The Unicorn and the Wasp - S4-E7
Continuity mistake: After the Doctor opens the Unicorn's case of tools, his right hand changes position when Greaves enters the room to deliver drinks. (00:22:20)
The Unicorn and the Wasp - S4-E7
Continuity mistake: After explaining that he's laced the soup with pepper, the Doctor, when he says, "Anyone got the shivers?", turns his head from looking to his left so he's looking in front of him. In the following wide shot, his head is turned to his left again. (00:26:10)
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: After the Doctor opens the secret door in the tunnel wall, he puts the sonic screwdriver into his inner jacket pocket. In the next shot he's in, as he says, "Now, what were you saying about running?", he does it again. (00:22:55)
Continuity mistake: When they get out of the TARDIS at the beginning, Martha and Donna change positions relative to each other between shots. (00:00:55)
Continuity mistake: During the conversation where Donna gives Jenny her name, Jenny's ponytail keeps changing position between draped over her shoulder and hanging in the back. (00:06:55)
Continuity mistake: When Donna suggests that she distract the next guard using her "womanly wiles", she flips her hair behind her shoulder. In the next shot, when the Doctor tells her to save her wiles for later, the hair has spontaneously moved to its former position. (00:19:35)
Continuity mistake: When the Doctor activates the teleport, Donna is onboard the Sontaran ship, holding a cell phone in her left hand. When she arrives in the basement of the ATMOS factory, she's holding the rubber mallet in her left hand, and her right hand is empty, with the phone nowhere to be seen. (00:32:40)
The Sontaran Stratagem (1) - S4-E4
Continuity mistake: When the clone Martha sits up in the tank, in a shot from behind her the umbilical cord is trailing down her back. In a shot facing her, it's draped over her shoulder, only to return to being down her back when she unplugs it. (00:35:20)
Continuity mistake: When the Doctor pulls out a TARDIS key to give to Donna, the exact position of the key in his hand changes between shots. (00:05:00)
The Sontaran Stratagem (1) - S4-E4
Continuity mistake: When Jo Nakashima says, "If you won't listen, I'll find someone else who will," she's holding her purse and bundle of papers in the crook of her left arm. When she opens the door of her car, the items have jumped to her right arm. (00:00:45)
The Sontaran Stratagem (1) - S4-E4
Continuity mistake: When Private Harris orders the two hypnotized workers in the basement of the ATMOS factory to let him through the door they're guarding, he's holding a torch in his left hand, and when shown from behind has that hand down by his side. In the Sontarans' video feed, which also shows him from behind, his left hand is on his assault rifle. (00:11:15)
The Sontaran Stratagem (1) - S4-E4
Continuity mistake: When General Staal surprises Privates Harris and Grey in the room with the cloning tank beneath the ATMOS factory, the position of his right hand, holding his command baton, changes between shots several times. (00:14:10)
The Sontaran Stratagem (1) - S4-E4
Continuity mistake: When Martha asks the Doctor to look at her so she can point out she's not carrying a gun, he's sonicing an ATMOS device, and he lowers his hand when she speaks. In the next shot facing Martha, the Doctor's hand is raised again. (00:16:10)
The Sontaran Stratagem (1) - S4-E4
Continuity mistake: When the Doctor gets embarrassed as Donna lightly mocks him for not realizing that when she said she wanted to go home, she only meant for a brief visit, he rubs his chin with his left hand. When Ross Jenkins interrupts by saying, "Ready when you are, sir," the Doctor is now rubbing his chin with his right hand. In the shot after that, it's back to his left hand. (00:20:40)
Continuity mistake: When the Doctor opens a shipping container full of Ood and he and Donna stand in the entryway, he only opens the right-hand door, leaving the other one shut. In a shot from behind the two of them, facing into the crate, the left-hand door is now wide open. (00:17:15)
Continuity mistake: When the Doctor and Donna enter Warehouse 15 and see the Ood Brain, the Doctor rests his hands on the railing with his right hand off to his side. In shots from above and behind him and Donna, his right hand is closer to him. (00:35:30)
Continuity mistake: When Ood Sigma steps in front of Mr. Halpen while he's holding the Doctor and Donna at gunpoint and suggests he have a drink, the glass Sigma holds up is empty, despite the fact that he was heard pouring Halpen's tonic into it just moments before. In a shot later in the scene, the glass is shown full. (00:37:30)
Continuity mistake: For most of the scene where the Doctor and Donna find the dying Ood Delta-50, the front of his body is covered in snow. After he mentions "the circle", when the Doctor is asking what that is, the snow on Delta-50's chest is gone. In addition, the Doctor's hands change position between shots. (00:06:25)
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.