Continuity mistake: When the Doctor and the housemates in the Big Brother house are watching TV, the brand name of the TV - Sony - appears in some wide shots, but is absent in other wide shots and all close-ups. (00:14:10)
Continuity mistake: As the Doctor, Captain Jack and Lynda with a Y have been captured, the Doctor turns his head to the right, then after it cuts it shows him turning his head again and saying "Let's do it." (00:32:05)
Continuity mistake: Just after they break out of the prison cell, you see Lynda reach for her gadgets twice. (00:32:20)
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.