Continuity mistake: When Martha, Milo and Cheen are talking in the powered-down car, the lighting changes between wide shots and individual close-ups.
Continuity mistake: After the Doctor gets directions to the motorway, when the red-haired female pharmacist leans over her counter to try and persuade him to buy some Happy, her hands change position between shots. (00:08:00)
Continuity mistake: When the Doctor, after being placed on hold while attempting to call the police, talks to Brannigan and Valerie about other people he could contact, in close-ups, Valerie has her right hand resting on the top of her seat. In a wide shot, she lowers her hand, but in the next close-up of her, it's jumped to its previous position. (00:14:20)
Continuity mistake: After Milo and Cheen abduct Martha, they put a sleep patch on her before entering their car. In the close-up where Cheen applies the patch, it's stuck on securely and neatly, with the top and bottom of the square pointing directly at Martha's head and chest respectively. In a wide shot immediately afterwards, the patch is stuck on quite loosely and has gone askew. (00:06:35)
Continuity mistake: In the episode "New Earth", the Doctor said that the titular planet is in the galaxy M87. Upon returning to New Earth in this episode, he says that the planet is 50,000 light-years from where the original Earth used to be. That's a difference of over 50 million light-years, since M87 is a very real galaxy in the centre of the Virgo Cluster, that far away from the Milky Way. (00:02:55)
Continuity mistake: The registration of Milo and Cheen's car is shown on the computer screen and stated aloud as "4-6-5-◊-6." However, there is a shot of Martha and Cheen looking out the window where the car's registration sticker is visible, showing a different registration: "9-9-6-γ-1." (00:13:15)
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.