The Impossible Astronaut - S6-E2
Revealing mistake: When the Doctor is struck by the green light emitted from the astronaut, his right thigh momentarily disappears due to the animation. (This is even more visible when looking at the still of this shot on the Doctor Who website). (00:07:06)
Revealing mistake: When the landlord, Purcell, wakes up on his floor because his pet dog is licking his hand, we see a few pieces of dog food fall from his fingers - should have been a re-shoot, but all credit to the actor, he knows it has happened and is quick to hide them again. (00:38:38)
Revealing mistake: When River grabs a gun off one of the soldiers she just knocked out with regeneration energy, the actor sits up slightly, even though the soldier is supposed to be unconscious. (00:24:44)
Revealing mistake: When the girl raises her visor to reveal herself in the spacesuit, the cracks in the visor from where it was shot earlier are drawn on. (00:20:22)
Revealing mistake: When the Cybermat gets free after the Doctor tries to hit it with a pot and accidentally gets Craig instead, it is very obviously CGI when it slides along the floor and stops by a piece of furniture. (00:26:34)
A Good Man Goes to War - S6-E8
Revealing mistake: Several of the hallways in Demon's Run, particularly the one where Madame Kovarian has the baby brought to her and the one the Doctor's standing in when he realises where Amy and Rory's baby was conceived, are the repainted sets of the TARDIS hallways from "The Doctor's Wife", three episodes before.
Revealing mistake: Mels is shot in the stomach by Hitler, leading to her regeneration. Rory, when checking the wound, says he's going to try and stop the bleeding. However, when she stands up while glowing with regeneration energy, and in every scene afterwards where Mels/River is wearing that dress, there is no bullet hole or bloodstain visible.
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.