Continuity mistake: When the Eleventh Doctor is hanging from the TARDIS across London, every wide shot shown shows the TARDIS spinning, but whenever a close-up of the Doctor is shown, the background doesn't spin. (00:00:20)
Continuity mistake: When Amelia comes out of her house with a torch to look at the crashed TARDIS, its exact position in her hand changes between shots a few times. (00:03:30)
Continuity mistake: As the Doctor stares down at young Amy, he takes a perfectly red apple from her and bites it. When the angle changes, and he spits the bite out, the apple has changed to an ordinary red and green one. (00:06:05)
Continuity mistake: After the Doctor spits out some yogurt that Amelia gave him and wipes off his mouth, there's still some yogurt on his face and chin. Immediately afterwards, he involuntarily jerks around a bit due to regeneration sickness, and the yogurt is gone. (00:06:35)
Continuity mistake: At one point while the Doctor is explaining to Amelia what the crack is, there's a shot where he has his hands on the wall examining the crack as he leans over Amelia's desk, then the camera cuts to a shot of Amelia where the Doctor is standing upright with his hands not touching the wall at all. (00:10:15)
Continuity mistake: When Mrs. Angelo and Jeff recognize the Doctor, leading to him learning that Amy was known for drawing cartoons of him when she was younger, he keeps changing position between shots. (00:30:05)
Continuity mistake: After the Doctor says, "Hang on, I missed it!" he smacks his head a couple of times and leaves a red mark on his forehead. When he turns his head immediately after that and says, "I saw," the red mark is no longer there. (00:32:35)
Continuity mistake: When the Doctor throws his hands in the air and exclaims, "Who da man!?", Rory's phone, which he was holding in the shots immediately prior, is missing. (00:47:25)
Continuity mistake: After Prisoner Zero is taken away, when Rory asks the Doctor if everything is back to normal, the Doctor is holding Rory's phone in his right hand while dialing a number. In the shot immediately after, focusing on Rory, where the Doctor walks by him and lightly smacks him on the shoulder, the phone is suddenly in the Doctor's left hand. (00:50:20)
Continuity mistake: During the scene on the hospital roof, when the Doctor is telling off the Atraxi while simultaneously choosing a tie out of several he stole from the locker room, the number of ties draped around his shoulders and the position of his hands changes between shots. (00:52:35)
Continuity mistake: After the Doctor steps through the hologram of his past selves and introduces himself to the Atraxi, in a wide shot, there's a red jacket lying on the ground to the left of Rory. In a close-up of Amy and Rory immediately following, the jacket has suddenly leaped into Rory's arms, to join the other clothes he's holding. When the Atraxi flies away, the red jacket is back on the ground again. (00:53:55)
Continuity mistake: At the end of the hospital roof scene, as the Atraxi are flying away, the Doctor is seen reacting to the TARDIS key in his jacket pocket heating up twice. (00:54:20)
Continuity mistake: After the Doctor brings Amy onto the TARDIS, the material of the tweed jacket he's wearing is entirely different in the close-ups of the Doctor's hands, as he's fiddling with the gears on the panel. (00:59:45)
Continuity mistake: Generally, it seems like it's cloudy on a rooftop, or Atraxi ship is making a shadow on it, but for one moment, after Doctor comes through the hologram, we can see bright sun and a shadow of construction behind the camera.
Continuity mistake: As Amy first enters the TARDIS, the Doctor comes up from her left, says his line, and leaves from her left. When the angle changes, he passes in front of her from her right.
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.