Other mistake: At the end, the Doctor and Rose treat Charles Dickens by making the TARDIS dematerialise in front of him. The engines begin to grind, but the time rotor (the thing in the console's central column that goes up and down when the TARDIS is flying) does not move. (00:42:53)
Other mistake: After Jack uses Davitch's information to complete the Controller's coordinates, the Doctor uses a remote to project a holographic, transparent screen of the location in question. The image shows Orion's Horsehead and Flame Nebulae. In a shot immediately afterwards, looking through the holo-screen back at the Doctor and company as he explains what's going on, the image of the nebulae is not mirror-reversed as it should be, but is the same orientation as in the previous shot. The kicker is that the image of the nebulae has been altered, as well: it's already been mirror-reversed - in the actual sky, the Flame is left of the Horsehead. (00:38:40)
Other mistake: When Mickey is trying to pull away from the trash bin, you can see his shadow on the front of his car, but the sun is shining from behind him and the car.
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.