Continuity mistake: When Idris reveals she's the TARDIS and the Doctor disbelieves it, her right hand moves between shots while it's resting on the bars of her cell. (00:16:32)
Continuity mistake: As the Doctor talks to Idris/TARDIS, he reaches into his coat. When the angle changes, he reaches in again. (00:18:20)
Continuity mistake: When Idris/TARDIS starts to run out of the room only to stop, grunt in pain and put her hand to her side, the hand in question switches from her right to her left between shots. (00:20:41)
Continuity mistake: When Idris/TARDIS tells the Doctor he's like a kid trying to rebuild a motorbike who never reads directions, her arms change position and the circuitboard she's holding switches hands between a close-up and following wide shot. (00:23:41)
Continuity mistake: When Idris/the TARDIS stumbles in the junkyard and the Doctor catches her, just before she tells him that one of her kidneys has failed, her right hand, holding a piece of circuitry, moves between in front of his chest in shots facing him and resting on his shoulder in shots facing her. (00:24:48)
Continuity mistake: After Rory receives the telepathic message, when he tells Amy what happened, his left hand jumps between rungs of the ladder he's climbing. (00:30:20)
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.