Forest of the Dead (2) - S4-E9
Continuity mistake: After the Doctor tints Anita's visor, as he explains to River that he did it to try and trick the Vashta Nerada into thinking they're already inside Anita's suit, the position of his right hand, holding the sonic screwdriver, and the fingers of that hand change position between shots. (00:10:25)
Forest of the Dead (2) - S4-E9
Continuity mistake: When the Doctor realises that the Vashta Nerada infesting the Library came from the books, he rubs the back of his head with his right hand, with his left hand in his trouser pocket. When Other Dave speaks, and the Doctor turns to him and discovers he's been eaten, he takes his left hand from the back of his head, with his right hand in his pocket. In the shot after that, his left hand is back in his pocket with his right hand in position as if he'd removed it from the back of his head. (00:18:30)
Forest of the Dead (2) - S4-E9
Visible crew/equipment: When River punches the Doctor, laying him out, just as he drops to the floor we can see the actor's green tape mark at River's feet. (00:33:20)
Forest of the Dead (2) - S4-E9
Continuity mistake: Near the end of "Silence in the Library," a sweeping shot shows that they're standing between two freestanding bookshelves. But at the beginning of this one, when they're supposed to be in the same place, they're able to break through a wall into a separate room.
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.