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)
Revealing mistake: At the end when Sarah Jane is walking towards the TARDIS and the Doctor opens the doors, the inside of the TARDIS is obviously a painting. (00:39:00)
Revealing mistake: During the scene in which the Doctor is climbing the transmitter, there is a shot in which he is viewed from above and is then struck by lightning. In this shot, the Doctor's foot disappears briefly as it leaves the green screen on the ground under the actor. (00:38:25)
Revealing mistake: When the Doctor calls Rose when she is with the Daleks, you can see on the screen of her phone that the call has been going on for at least 57 seconds, but she just answered the call. (00:06:50)
Revealing mistake: In the Torchwood building, a large group of Cybermen start shooting at the Daleks and the Genesis Ark. The Daleks shoot several of them, and you can see a Cyberman that, thanks to hilarious CGI, just collapses like a sock without any physical regard that he is wearing tough metal leg armour, is floating a little off the ground, and falls way too fast than physical laws could allow. (00:25:15)
Revealing mistake: When the Doctor and Rose are talking at the bay, the Doctor's hair is blowing in the wind, but it's not when he is shown in the TARDIS. Considering the image of him on the beach is a projection of him in the TARDIS, the two versions should match. The actor was obviously on the beach recording his lines with Rose and back on a set doing the inside scenes.
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.