Continuity mistake: As Lucy goes down the hall, she opens door 214, then 215. As she comes to the next door on the right, she opens 214 again, rather than it being 216. This is particularly noticeable because the third room she enters is "her" room, containing her greatest fear - and the first room she went into numbered 214 had a completely different fear. (00:00:56)
Continuity mistake: When the Doctor tells Howie that he should continue telling himself the situation is a "CIA thing", he puts his arm around his shoulders twice. (00:11:22)
Continuity mistake: When the Doctor finds Joe's corpse, he walks up to him and puts his hand on his shoulder. In the next shot, facing Joe, the Doctor is suddenly in a completely different position relative to him, behind him as opposed to next to him. (00:15:06)
Continuity mistake: During the Doctor's phone conversation with Rita, the handset of her phone keeps switching between ears. (00:32:30)
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.