Visible crew/equipment: As Sally enters the living room in the abandoned house, in the shot where she walks through the doorway, a cameraman holding the camera can be seen reflected in the window of the door next to her. (00:00:35)
Continuity mistake: When Sally pulls off the last piece of wallpaper to reveal the writing, "Love from the Doctor (1969)", in the first shot, the second "9" in the date is somewhat patchy, with the middle part of the number mostly gone due to the removal of the wallpaper. In a close-up of "The Doctor" just moments later, the "9" is intact, visible in the lower right corner. (00:02:15)
Continuity mistake: When Sally Sparrow is about to take the key from the weeping angel, at first the key is on a piece of string, and that string is wrapped around the weeping angel's left hand. In the next shot, and when she pulls the key out, the string is now only in the angel's palm. (00:10:30 - 00:11:10)
Continuity mistake: When Sally enters the DVD store looking for Larry, she encounters the store's owner, Banto, who is sitting behind the front counter watching a movie. He holds up his finger to indicate her to wait briefly because of the point in the movie he's at. In shots facing him, his hand is quite close to his mouth and chin, but in a shot facing Sally, his hand is considerably further away from his head. (00:13:10)
Continuity mistake: When Sally picks up the remote to pause the recording of the Doctor after getting unnerved by him seeming to hear her, and when she rests it against her forehead after Larry comes back into the room, it switches between her hands a few times. (00:16:40)
Audio problem: While Billy Shipton is showing Sally Sparrow the TARDIS (in the room where he keeps the abandoned cars), just after he says, '[You] can't even get in it', he rattles the TARDIS' handle to demonstrate. Watch carefully: When he shakes the handle we hear a rattling noise as if the door is shaking, but in fact the door stays rock solid. (00:19:35)
Continuity mistake: After Sally leaves the garage, Billy turns his head and sees the Weeping Angels around the TARDIS, and his facial expression changes from a smile to a confused frown. In a close-up of Billy after the shot of the Angels, his head is turning and his expression changes a second time. (00:20:40)
Continuity mistake: When Sally is holding the picture of Billy and his wife, the position of her right index finger on the frame changes between shots. (00:24:35)
Continuity mistake: When Sally takes out the list of DVDs while talking to Billy in the hospital, her grip on the paper changes between shots. (00:25:40)
Continuity mistake: When Lawrence is watching the Weeping Angel, just after seeing the Doctor's film/Easter egg, he turns away for a split second. By the time he turns back, you see the Weeping Angel's face only inches from Lawrence's face. But you then cut to a wide shot where you see the Angel's arms outstretched, so its face is about half a metre away from Lawrence's face. (00:34:45)
Continuity mistake: When Sally and Larry are hugging each other as the TARDIS dematerializes around them, as the cellar with the Angels becomes more visible, Sally lets go of the console with both hands and clasps them together. A couple of shots later, her left hand is still touching the console. (00:37:55)
Other mistake: When Sally is taking the key from the angels, she squats down out of the frame to reveal an angel behind her that has lowered its hands from its face. When the shot cuts back to Sally, there is another angel standing in front of the window on the other side of the room whose hands are also lowered from its face. The two angels with lowered hands are directly across from each other: they should have been frozen in place from this point due to their quantum lock.
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.