The Christmas Invasion - S2-E2
Revealing mistake: After the Christmas tree has cut through the wall in the Tylers' flat, you can see marker pen where the shape has been drawn and cut out. (00:10:30)
The Christmas Invasion - S2-E2
Revealing mistake: In the scene after the Christmas tree has been destroyed in the flat and the Doctor, Rose, Jackie and Mickey are standing outside, the robot Santas do not have any gloves on, showing human hands. (00:11:05)
The Christmas Invasion - S2-E2
Revealing mistake: When Daniel Llewellyn is looking up U.N.I.T. staff records on the computer, at one point a control panel for a DVD playing program is visible onscreen, showing that the special U.N.I.T. user interface is a video. (00:26:25)
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.