In the Forest of the Night - S8-E10
Continuity mistake: When Clara is looking at the drawing in Maebh's homework book while the Doctor tells her about the solar flare, her grip on the book changes between shots. (00:22:44)
Dark Water - S8-E11
Continuity mistake: When it's revealed that the dream patch is on Clara's hand, it's in her right palm. But in the wide shot when she's getting up as the Doctor explains the true nature of the patches, it's on her left hand instead. (00:13:21)
Dark Water - S8-E11
Continuity mistake: As Clara nods and says "Fair enough" when she thinks the Doctor has told her to leave, her arms go from crossed to by her sides between the closeup and the wide shot. (00:14:29)
Continuity mistake: When the Cyberman in the office locates Clara hiding behind the desk, its gun arm goes from stretched out to bent between shots. (00:00:46)
Continuity mistake: During the early scene with the Cybermen outside St Paul's, when Missy pulls out her phone/disintegrator weapon and shows the Doctor pictures of the Cybermen going viral all over the planet, and when she prepares to take a picture of the two of them, her grip on the device, as well as which hand she's holding it in, keeps changing between shots. (00:03:00)
Continuity mistake: Missy's cameo brooch is unpinned and hanging askew when she vaporizes Osgood, but the brooch rights itself and is pinned properly when Missy steps on Osgood's eyeglasses. (00:23:00)
Continuity mistake: When Missy orders her Cybermen to blow up the plane and kill some Belgians, her control bracelet is missing from her wrist in one shot. (00:33:54)
Continuity mistake: When the Doctor hands out of the base manuals to the expedition crew for the dream test, Albert Smith is shown with his manual open in shots from behind him several shots before he's shown opening it in a shot facing him. (00:35:56)
The Magician's Apprentice - S9-E2
Continuity mistake: When Colony Sarff arrives at the arena, he's seen unclasping his hands twice, in the close-up and following wide shot. (00:28:38)
The Magician's Apprentice - S9-E2
Continuity mistake: During the exchange where the Doctor says "You flatter me" and Davros responds "A pity. I intended to accuse", Davros' hand goes from just under his chin to resting on his chair's control panel. (00:40:15)
Continuity mistake: At the beginning, Missy is using a knife to sharpen a stick to a point. Later in the scene, when she says to Clara that if they go rescue the Doctor, everything the Daleks can throw at them is between them and him, she lists only the stick among their assets. The knife is never seen or mentioned again after Missy was done with it. (00:04:18)
Continuity mistake: After Missy hooks Clara up to the Dalek armour, she takes her hands away from Clara's temples. However, in shots facing her for the next several shots until she stands up and backs away, her arms are still raised. (00:22:24)
Continuity mistake: Davros' chair has metal parts which go over his shoulders - they are attached to the chair, not Davros. When the Doctor steals Davros' chair they disappear, but when Davros is back in it they have reappeared.
Continuity mistake: When the Doctor is listing questions about what exactly the ghosts are, he goes from gesturing with his left hand in the close-up to gesturing with his right in the wide shot. (00:17:17)
Continuity mistake: For most of the robbery sequence at the beginning, the Nightmare (a disguised Ashildr) is holding her pistol in her right hand. When she's yelling at the Doctor for interfering with her robbery while he's looking at the chest strapped to the back of the carriage, however, she's holding it in her left hand. It switches back to her right after the carriage escapes.
Continuity mistake: When Bonnie is filming the transformation of the Zygon man who she stripped of control over his shape, her grip on the phone she's using changes between shots.
Continuity mistake: When Bonnie throws the laptop with the Osgoods' message to the floor and stomps on it, the computer's position changes between shots - take note of the tape markings on the floor. In addition, the position of the plastic frame of the laptop's screen changes: in the first shot, it's mostly popped out, but in the second shot, it's mostly attached.
Continuity mistake: When Bonnie gets a video call from the Doctor, her grip on the phone changes between shots.
Continuity mistake: When Clara takes Rigsy's chronolock, in the closeup of the tattoo Clara's lifting her hair with her right hand and showing the tattoo with her left hand, but in the next front-facing shot her hands have switched, she's holding up her hair with her left hand and showing the tattoo with her right hand. (00:26:45)
Continuity mistake: When the Shade leaves Clara and she falls, her body is twisted because of the way her legs are bent with one on top of the other and her arms are out to the side. In the overhead shot of her, her positioning has changed, her body isn't twisted and her arms are more straight down her side.
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.