The Doctor, the Widow and the Wardrobe - S7-E1
Revealing mistake: When Cyril is walking around the statue and chair in the tower, if you look closely you can see the statue's hands move or shake. (00:30:14)
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)
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)
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)
The Snowmen - S7-E7
Revealing mistake: When the Doctor and Vastra are on the TARDIS talking about Clara's injuries, and he says that he thinks for once the universe owes him one, he pulls some switches on the console. If you pay attention, you'll notice that the console wobbles slightly as he does so. (00:49:48)
The Bells of Saint John - S7-E8
Revealing mistake: During the sequence where Clara sets foot on the TARDIS for the first time, and she and the Doctor then stop the plane from crashing, there are some shots which make it fairly obvious that the mug of tea she's carrying is empty. (00:25:35)
Revealing mistake: While the Doctor and Clara visit the market in Akhaten, the rubber mask of one of the aliens they encounter is revealed, as the eyes of the actor wearing it are very much visible. (00:08:10)
Revealing mistake: Just before Strax leaves grumbling that he's going to play with his grenades, if you look closely you can see his face mask peeling. (00:27:45)
The Day of the Doctor - S7-E16
Revealing mistake: When Osgood tells Kate that they're using Derren Brown as the explanation for flying the TARDIS into Trafalgar Square by helicopter, the two women are standing in front of the TARDIS. Its door is slightly open, revealing an interior that is obviously a picture. (00:05:00)
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.