Dinosaurs on a Spaceship - S7-E3
Revealing mistake: The Doctor tells everyone to run, which they do. As they go around a corner in the distance, the actors at the rear of the group, presumably believing themselves out of shot, slow to a trot. (00:05:04)
Dinosaurs on a Spaceship - S7-E3
Continuity mistake: After Rory and Brian are sitting in the control chairs, when the Doctor makes a Silurian joke and then gripes that no-one found it funny, Brian's hands move to the buttons on the end of the armrests instantaneously between shots. (00:39:20)
Dinosaurs on a Spaceship - S7-E3
Continuity mistake: At the end Amy and Rory receive a postcard from Siluria with the TARDIS pictured on it, but it is the old TARDIS from 2005 (note there is no St John's ambulance sign on it). (00:46:02)
Continuity mistake: During the sequence involving Rory and Isaac leaving town with the latter disguised as Kahler-Jex in order to distract the Gunslinger so the Doctor can get back to the TARDIS, parked somewhere outside of Mercy, only to find Jex's ship instead, while Amy and Jex wait back at the sheriff's office, the Sun changes position several times, as do the shadows cast as a result. Most noticeably, when the Doctor finds the cable running from Jex's ship to town, the Sun is quite low, as if close to sunset - while appearing high, as if closer to midday, in the scenes of Rory and Isaac distracting the Gunslinger taking place at the same time. During the scenes of the Doctor finding Jex's ship and Amy and Jex in town, it is also earlier in the day. (00:10:50 - 00:17:17)
Continuity mistake: When Amy's holding a revolver while arguing with the Doctor, just before she accidentally fires it a second time, she goes from holding it pointed to her right to holding it pointing to the ground in front of her between shots. (00:23:53)
Factual error: During the standoff after the Doctor forces Jex over the town's boundary line, Amy manages to make a revolver accidentally fire off twice in a row. Revolvers like that need to be cocked between each firing, which didn't happen the second time. (00:23:54)
Continuity mistake: When Amy and the Doctor are arguing over whether Jex should be punished, her hair is blowing a lot in shots facing him, but very little in shots facing her. (00:24:10)
Continuity mistake: The scene where the Doctor forces Jex over the boundary line starts off in roughly mid-afternoon lighting, but when the Gunslinger arrives and Isaac is shot, the sunlight is at a much lower angle. (00:25:35)
Revealing mistake: When Jex's ship explodes, we see the smoke drifting over town. But it's really obvious that the smoke is coming from the next street, not miles away where Jex's ship is. (00:42:06)
Other mistake: As the Doctor passes a stack of three cubes, the camera is close enough to see the top cube has two small squares intertwined on the side facing diagonally toward the light. He said all were the same, no difference or individuality whatsoever. (00:03:53)
Visible crew/equipment: When the Doctor is painting the fence and vacuuming the living room, Amy lifts her legs to let the Doctor pass with the vacuum, revealing the transmitter for her mic in her back pocket. (00:07:45)
Continuity mistake: As the Doctor is saying "Pudding, but savoury: sound familiar?", the fish finger he's holding suddenly has less custard on it between shots. (00:16:25)
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)
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.