Continuity mistake: When Gadget is driven to the TARDIS so the Doctor can retrieve it, the landscape around it is much flatter and without the large boulders strewn around the TARDIS when the Doctor arrived on Mars at the beginning. (00:52:41)
Continuity mistake: When the Doctor leans on the railing above the glacier while telling Adelaide about the Ice Warriors, he rests his left hand a ways out on the railing, in a spot where it should be visible but isn't in the next shot from behind him. (00:28:57)
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.