Continuity mistake: When Cassandra, after possessing Rose, is checking out her new body in a mirror, when she starts jiggling up and down, her right hand changes position between shots of her and shots of her reflection. (00:13:40)
Continuity mistake: When Cassandra, possessing Rose, answers her phone, as Chip is telling her that Rose's accent is "Old Earth Cockney", she puts the phone to her ear twice. (00:14:55)
Continuity mistake: When Cassandra reveals her presence to the Doctor, she starts off by turning him to face her, then pulling his tie out of his jacket with her right hand and tightening the knot with her left hand, in a shot facing him. In the next shot, facing her, she has her right hand holding the knot of the tie. Finally, just before Cassandra reveals her identity to the Doctor, shortly later, which hand is holding the tie changes again. (00:23:20)
Continuity mistake: When Cassandra, possessing Rose, confronts the Doctor after he wakes up in one of the clone pods and tells him how she intends to kill him, her hand changes position between the shot from inside the pod, when she rests her hand on the front, and the next shot from outside the pod. (00:24:20)
Continuity mistake: When Rose gets into one of the hospital's elevators early in the episode, stock footage of an elevator descending is shown. When the Doctor, Rose and Cassandra (possessing her) go into an elevator shaft later on, it looks and is shaped completely differently. (00:34:05)
Continuity mistake: When the Doctor is attaching the ring device to the elevator cable, the position of his hand as he's holding it in place changes. (00:34:10)
Plot hole: Those people created for medical experiments cannot run. In fact they can barely walk, so how come they can climb nearly as fast as Rose? What's more, when you see them climbing, they seem to have little ability to coordinate hand over hand. Even with the delay brought on by the cat-woman-thing, they should not have been able to keep up with her.
Continuity mistake: When Chip/Cassandra finishes the line about being a walking doodle, he's smiling. After the cut, he's straight faced.
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.