Other mistake: When Jenny does somersaults through the laser beams, the last two beams are level horizontally and the higher beam is lower than her foot, so she should have broken it.
Other mistake: Martha falls into the bog and Hath Peck rushes down to help her. She calls out "Help me, Peck!" but the subtitles read "Help me peg!" This is just one of many errors in this series' subtitles, which seem to have been added by listening to the dialogue without reference to the script. (00:26:30)
Continuity mistake: When the Doctor starts scanning the wall of the tunnel as Jenny asks him who he is and if he's an anomaly as well, his grip on the sonic screwdriver changes between shots. (00:22:20)
Continuity mistake: After the Doctor opens the secret door in the tunnel wall, he puts the sonic screwdriver into his inner jacket pocket. In the next shot he's in, as he says, "Now, what were you saying about running?", he does it again. (00:22:55)
Continuity mistake: When they get out of the TARDIS at the beginning, Martha and Donna change positions relative to each other between shots. (00:00:55)
Continuity mistake: During the conversation where Donna gives Jenny her name, Jenny's ponytail keeps changing position between draped over her shoulder and hanging in the back. (00:06:55)
Continuity mistake: When Donna suggests that she distract the next guard using her "womanly wiles", she flips her hair behind her shoulder. In the next shot, when the Doctor tells her to save her wiles for later, the hair has spontaneously moved to its former position. (00:19:35)
Continuity mistake: In the scene where Cobb is briefing his troops, the troops all have their guns, but in the other scene (after you see the Hath marching) the troops are receiving guns. (00:15:45)
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.