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.
Continuity mistake: When Amy's dad stands up to present his speech at her wedding, a tear runs down the right side of Amy's face. In the next shot of her the right side of her face is completely dry.
Continuity mistake: When little Amy looks out the window to see what makes the noise, you can see the TARDIS through her window (it's a little blurry) but when you look through the window properly, it isn't there.
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.