Audio problem: Just after the Doctor makes his appearance and Lynda tells him he's "in the house", she appears to continue talking to him but we never hear what she says; instead the scene cuts to the other two housemates complaining about the Doctor's sudden appearance. (00:01:40)
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)
Revealing mistake: When the Gamestation's transmissions are cut off by solar flares, there is a close-up of a screen going over to static. In the upper right corner, a box with "Play" written in it is visible, revealing the image on the screen as a video. (00:34:50)
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)
Factual error: The Doctor claims the Daleks are hiding themselves from sonar. But sonar relies on sound waves, which can't travel through the vacuum of space. (00:38:45)
Revealing mistake: After the Doctor deactivates the signal hiding the Dalek fleet, when the camera zooms out to show the ships, the background image of the Horsehead and Flame Nebulae is cut off a bit below where the Dalek Emperor's flagship is shown, revealing the end of the picture they used for a background. (00:39:00)
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.