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: 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)
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: 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: 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 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)
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)
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)
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.