Revealing mistake: When Brian is woken up by the cube he was watching suddenly moving, the cube is obviously not lying flat on the table surface, being slightly tilted up in order to make room for the device being used to make it spin. (00:16:41)
Continuity mistake: When the Doctor is at the Tower of London with Amy and Kate, he claims he needs some air. When Amy follows him she follows him twice, in two different shots. The first time on 'ground view' walking and the second time on 'above view' running. (00:21:20)
Continuity mistake: When the Doctor is in the containment unit with a cube during the countdown, there's a shot from outside where another cube in another containment unit is in the background, not displaying the countdown that all of the cubes are supposed to be showing. (00:29:03)
Continuity mistake: When Rory finds his dad on the spaceship, Brian is lying on a gurney next to the two farthest slabs, which are empty. When Amy and the Doctor come through the portal to the spaceship, Brian's gurney is between the two closest slabs, with Rory lying on the closest one, which previously had a completely different person lying on it. (00:35:05)
Continuity mistake: When the Doctor is telling Amy and Rory how he's going to reprogram the cubes, the sonic screwdriver disappears from his hand. (00:38:50)
Continuity mistake: After the Doctor reprograms the cubes, when he tells Amy and Rory that a massive energy wave is about to go through the spaceship, his right hand, holding the sonic, goes from raised to lowered. (00:39:20)
The Angels Take Manhattan - S7-E6
Continuity mistake: As the Doctor explains about the book he's reading, he goes from holding it with one hand to two between angles. (00:07:19)
The Angels Take Manhattan - S7-E6
Continuity mistake: When the Doctor comments on Amy and Rory kissing in public before Rory leaves to get coffee, he goes from holding his book in his lap to reading it and back between shots. (00:08:15)
The Angels Take Manhattan - S7-E6
Continuity mistake: When Amy and Rory are arguing after he puts her left hand to his chest and she grabs his shirt, in close-ups of her, she has her right arm raised instead. (00:36:00)
The Angels Take Manhattan - S7-E6
Continuity mistake: When they are back in the cemetery at the end, the Angel shows up right behind Rory. In the first shot facing Rory, as the camera zooms in on a close-up of the Angel, the Angel's right arm/hand is pointing straight out, and its left open hand is up in a grabbing position. After River asks where the hell it came from, in the Angel's next close-up and all subsequent close-ups, its arm/hand positions are reversed - left hand is pointing straight out and its right hand is up. Yet in every shot of the Doctor, River and Amy together, in the foreground we see the Angel's left hand is up in the grabbing position. (00:37:35)
The Angels Take Manhattan - S7-E6
Other mistake: The photo shoot PA from "Asylum of the Daleks" earlier in this season isn't in the credits for that episode, but is credited in this episode, despite not featuring in it. (00:45:36)
The Snowmen - S7-E7
Continuity mistake: While confronting Dr. Simeon in an alleyway, when Vastra picks up some snow and remarks about how interesting it is, the fingers of the hand she's holding the snow with change from being extended to curled up and back again between shots. (00:08:58)
The Snowmen - S7-E7
Continuity mistake: When Clara tests the solidity of the cloud the TARDIS is parked on, her right hand suddenly jumps to the railing of the staircase between shots. (00:18:14)
The Snowmen - S7-E7
Continuity mistake: When the Doctor offers Clara a TARDIS key, he's holding it differently between shots. (00:44:35)
The Snowmen - S7-E7
Revealing mistake: When the Doctor and Vastra are on the TARDIS talking about Clara's injuries, and he says that he thinks for once the universe owes him one, he pulls some switches on the console. If you pay attention, you'll notice that the console wobbles slightly as he does so. (00:49:48)
The Snowmen - S7-E7
Continuity mistake: When the Intelligence in Simeon's body is attacking the Doctor, the Doctor's left arm goes from pushing at Simeon's right shoulder to suddenly stretched along the floor in a shot from above. (00:54:48)
The Snowmen - S7-E7
Continuity mistake: When the Doctor is explaining what the intelligence in the giant snow globe is, though enclosed, the amount of "snow" alternates from a fair mass to a few handfuls and back several times.
The Snowmen - S7-E7
Continuity mistake: As Clara first realises the differences in the TARDIS exterior and interior, she goes to circle the outside, leaving the door open. A second later, it's closed, but open upon her entrance.
The Bells of Saint John - S7-E8
Continuity mistake: When Clara is talking to Mr. Maitland as he prepares to leave, the cordless phone she's holding switches hands. (00:05:38)
The Bells of Saint John - S7-E8
Continuity mistake: When Clara takes the copy of Summer Falls away from Artie briefly, the position of her hand on the book changes between the initial shot and the close-up of the book's cover. (00:05:41)
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.