Continuity mistake: After the Doctor tells Bill that nothing gets through the TARDIS doors, when she responds that they're made of wood and have windows, the Doctor's left hand changes position between shots from being apparently by his side to suddenly resting on the door. (00:28:40)
Continuity mistake: When the Doctor holds out his sonic screwdriver for the Dalek to scan, his grip on it changes between shots. (00:42:25)
Continuity mistake: When Bill says to the Doctor, "Do what you gotta do," he raises his hands to her. His hands are closer to Bill's face in shots facing him than shots facing her. (00:48:40)
Continuity mistake: When the Doctor starts writing "Time" on the chalkboard during class, the "T" is slanted, but in a following wideshot when he's completed the vertical "TARDIS" the handwriting has changed. (00:08:10)
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.