Continuity mistake: When the Doctor finds the stolen cup inside Christina's knapsack, he's shown reaching for it twice, in the wide shot and the close-up. (00:38:40)
The End of Time: Part Two - S4-E18
Continuity mistake: When Wilf takes out his revolver and offers it to the Doctor, he's holding it with the grip pointed toward the Doctor. In a wide shot shortly afterwards, Wilf's arm is moving to hold the gun out again, this time with the barrel closer to the Doctor. In the next shot, a close-up of Wilf, the gun is back to its first orientation. (00:25:20)
The End of Time: Part Two - S4-E18
Continuity mistake: When Shaun and Sylvia run out of the Nobles' house to look as Gallifrey begins to phase in and out next to Earth, Shaun's right hand, which he had on Sylvia's shoulder, changes position between shots just before he runs off looking for Donna. (00:40:40)
The End of Time: Part Two - S4-E18
Continuity mistake: When Donna, on the phone with Wilf, is surrounded by Master duplicates in the alley behind her house, she has her phone to her ear, but there's a shot where she looks behind her to see two Masters, one of whom is wearing a bowtie, entering the alley, her phone is missing, only to be back by her ear in the next shot. (00:07:05)
Continuity mistake: After Lucy gets the bottle from the guard, as she explains to the Master that her family had contacts to create something to counteract the "potions of life" used to resurrect him, she starts to take the cork out of the bottle with her left hand, the camera cuts away to the Master and when it cuts back to Lucy, her left hand is on the bottom of the bottle, before she starts to take the cork out again. (00:15:00)
Forest of the Dead (2) - S4-E9
Continuity mistake: When the Doctor realises that the Vashta Nerada infesting the Library came from the books, he rubs the back of his head with his right hand, with his left hand in his trouser pocket. When Other Dave speaks, and the Doctor turns to him and discovers he's been eaten, he takes his left hand from the back of his head, with his right hand in his pocket. In the shot after that, his left hand is back in his pocket with his right hand in position as if he'd removed it from the back of his head. (00:18:30)
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)
The Unicorn and the Wasp - S4-E7
Continuity mistake: At the lake, when the Doctor stands in front of Agatha and tells the Vespiform, "You're not meant to be like this! You've got the wrong template in your mind!", in the close-up shot he has his left arm raised, but in the Vespiform's POV shot he has his right arm raised. (00:39:45)
The Unicorn and the Wasp - S4-E7
Continuity mistake: When Robina Redmond is announced, and Lady Eddison says, "She's the absolute hit of the social scene - a must," in the first shot, Lady Eddison is standing close enough to her wheelchair-bound husband to cast a shadow on him. In the second shot, the distance between them has suddenly increased. (00:05:10)
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)
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.