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)
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)
The Unicorn and the Wasp - S4-E7
Continuity mistake: When Agatha shows the Unicorn's case of tools to everyone when they're all gathered in the parlour, the case is shown open just before she's shown opening it. (00:29:50)
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: Thoughout the episode, Donna's rhinestone-studded hairband changes between going over or under her ears.
Silence in the Library (1) - S4-E8
Continuity mistake: When the girl recognizes the Doctor on her TV, telling him that he was in her library, and he reacts, the position of her pencil crayon in her hand changes between shots. (00:20:45)
Silence in the Library (1) - S4-E8
Continuity mistake: After Miss Evangelista is killed, we see her communicator as her "ghost" slowly fades. In one shot we see from a slight distance the lights left lit tick down to 3, then a short while passes, we cut back and the lights are back to 4. They then tick down to 3 again.
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)
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: Near the end of "Silence in the Library," a sweeping shot shows that they're standing between two freestanding bookshelves. But at the beginning of this one, when they're supposed to be in the same place, they're able to break through a wall into a separate room.
Continuity mistake: After the TV signal cuts out due to the crash of the Titanic, when Sylvia says "It's gone dead" while searching for a channel, she moves her arm with the remote forward the same as she did in the previous, wider shot. (00:18:57)
Continuity mistake: The house that Donna and her family are shown living in in Series 4 is different from the house the Doctor dropped her off at at the end of her first appearance, "The Runaway Bride." You would assume they'd merely moved - except that in this episode, Donna and her family are shown living in their Series 4 house before the events of "The Runaway Bride", on the day Donna gets the job that leads to her meeting the Doctor in the first place.
Continuity mistake: In this episode, Rose's teeth look different than in all her other appearances. She also has a different accent, both for no apparent reason.
Continuity mistake: Before Martha uses Project Indigo she doesn't have an ear piece. A shot later when she says, "Bye, Jack", she does (and then takes it out). (00:17:56)
Continuity mistake: When the TARDIS is breaking through the time limit to reach the stolen planets, the console room catches on fire from the strain. But after reaching its destination, the console room is abruptly back to normal. (00:35:05)
Continuity mistake: In the scene toward the end where the Doctor is shot by the Dalek, when the camera is shooting from Rose's point of view, the Doctor is gasping and struggling for breath. However when the camera shows the Doctor from behind, he's lying completely still in Rose's arms. The camera cuts back to Rose's POV and he's struggling again, with no time in between for the change in his movements. (00:43:35)
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.