Revealing mistake: When the Doctor travels back in time after being shot by the stone Dalek, falls down the stairs and tells himself that he has 12 minutes to live we never see either of the 2 Doctors' faces onscreen at the same time, and if you look at the hair on the Doctor that's dying it is completely different to Matt Smith's. That's because it is Gordon Seed, Matt Smith's stunt double.
Revealing mistake: When the Cyberman arm is shooting at the Doctor and Amy, just after the Doctor jumps out to draw its fire, Amy leans on the Pandorica and you can see it bend in, revealing that it's made out of plastic or something. (00:20:42)
The Vampires of Venice - S5-E6
Revealing mistake: When the Doctor begins climbing a pillar on top of the bell tower, we can see white sky on the central arch. Two other arches in the very same shot show really dark CG sky. (00:42:17)
Revealing mistake: When the Doctor's jacket is being held by a Weeping Angel while he's monologuing about why they haven't killed him yet, he moves at one point and the Angel's hand moves with him, despite the fact that they're normally effectively stone in situations like this. (00:12:16)
Revealing mistake: When an Atraxi ship appears over the village green, there's a shot where the Doctor, Amy and Rory turn to look at it, and they're standing in bright sunshine with their shadows visible - despite the fact that the Atraxi have surrounded the planet with a forcefield that dims sunlight, so those shadows shouldn't be possible. (00:36:05)
Revealing mistake: As Amy stands where she is told, a cable comes towards her feet. As it does, a black thread can be seen pulling it up to wrap around her leg. (00:21:39)
Revealing mistake: When the TARDIS dematerialises and causes wind to blow against Churchill and Amy, their clothes are affected - but the cigar smoke in the air is unaffected, and actually drifts towards the vanishing TARDIS. (00:14:25)
Revealing mistake: In the museum after the Doctor, Amy, young Amy and Rory escape the Stone Dalek, the Doctor uses the Vortex Manipulator to go back in time to tell Rory in 102 AD to let him out of the Pandorica. The third time he goes back, Amy moves despite being dead. (00:19:38)
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.