Revealing mistake: When they show the soldiers killed by the Dalek, in both the hallway outside the cage and the large room in weapons testing, they show some casings which were ejected from the soldiers' guns. The casings still have projectiles in them. If used, they would have been in magazines and would never fall out like they are shown.
Revealing mistake: When the Doctor travels back in time after being shot by the stone Dalek, falls down the stairs and tells himself that he has 12 minutes to live we never see either of the 2 Doctors' faces onscreen at the same time, and if you look at the hair on the Doctor that's dying it is completely different to Matt Smith's. That's because it is Gordon Seed, Matt Smith's stunt double.
Revealing mistake: When the alien spacecraft crashes into Big Ben, it is obvious that the shot has been reversed/flipped around. Look at the Roman numerals on Big Ben's clock face: They should read (clockwise from the top) XII, I, II, III, and so. Instead they read IIX, IX, X, etc. (00:06:35)
Revealing mistake: The 'earthquake' that takes place in this episode results in CGI-created cracks in the pavement that are very unconvincing. They do not appear to displace anything and - in a related continuity error - the cracks disappear in shots taken from ground level (the cracks are only visible in high-level 'looking down' shots). (00:34:30)
Revealing mistake: The Doctor and Rose locate the "metal" hatch that leads down into the Nestene Consciousness' lair. Watch carefully after the Doctor removes the "metal" hatch and moves it aside. The entire hatch pops up a second later. This is because it is plastic and it was suctioned to the floor. (00:33:06)
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: Soon after the Doctor and Donna are blasted back there is fake snow on the camera, indicating there's a camera there. (00:34:15)
Revealing mistake: When the Cyberman arm is shooting at the Doctor and Amy, just after the Doctor jumps out to draw its fire, Amy leans on the Pandorica and you can see it bend in, revealing that it's made out of plastic or something. (00:20:42)
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.
Revealing mistake: When Mickey closes the wheelie bin lid, he then finds the plastic stuck to his hands, he lifts his hands up and the plastic stretches like tar. If you look closely when he lifts his hands up for the first time, you'll see that a shadow of one of his hands is cast on his shirt, but there is no shadow of the strands of plastic stuck to his fingers. Additionally, when he turns around to pull away from the bin, he crosses the strands over each other, but they are still parallel in the following scene. (00:22:40 - 00:23:10)
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)
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: In the close up shot of the boys' machine guns firing, in the background a white truck can be seen driving across the green countryside; not appropriate for the time period of the story. (00:25:25)
Revealing mistake: While the Doctor and Clara visit the market in Akhaten, the rubber mask of one of the aliens they encounter is revealed, as the eyes of the actor wearing it are very much visible. (00:08:10)
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)
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: At the end of the episode there is a side shot of the Doctor leaving the TARDIS in which you can see inside, but the control room isn't visible, just the side of the police box, with light from outside shining through the window. (00:38:00)
Revealing mistake: In close-ups of the modified pig, seams are visible on its forelimbs. (00:22:45)
Evolution of the Daleks (2) - S3-E5
Revealing mistake: When Dalek Sec picks up the remains of the radio and turns it in his hands, the "Hamilton" label on the front of the radio is written backwards, indicating that the shot has been flipped horizontally. (00:05:00)
Evolution of the Daleks (2) - S3-E5
Revealing mistake: When the people in Hooverville are meeting around the campfire, it's raining. However, everyone's clothes and hats are completely dry. (00:28:05 - 00:28:45)
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.