Revealing mistake: When the Doctor goes to toss the trio of Christmas balls up, the two times after the first toss are re-used shots of the first toss. His movements of his right arm to bring up the controller are too exact to be coincidence. (00:50:15)
Revealing mistake: As Amy stands where she is told, a cable comes towards her feet. As it does, a black thread can be seen pulling it up to wrap around her leg. (00:21:39)
The Sontaran Stratagem (1) - S4-E4
Revealing mistake: In the beginning, the ATMOS system takes the car to the Thames, then runs it into the river. At first, the car runs forward normally. After the angle change, there's a huge white cloud of mist behind the car that dissipates quickly, meaning an air cannon of a sort was used to propel the car into the river. (00:02:35)
The Doctor, the Widow and the Wardrobe - S7-E1
Revealing mistake: When Cyril is walking around the statue and chair in the tower, if you look closely you can see the statue's hands move or shake. (00:30:14)
Revealing mistake: When the old man is stabbed, the sword is retracted and we can see there is no blood visible on the sword. This is visible even before the blood is wiped off. (00:06:55)
The End of Time: Part Two - S4-E18
Revealing mistake: When Addams is telling Rossiter not to respond the Master's message, a patch of non-green skin can be seen on her face showing where the makeup wasn't fully painted on. (00:27:50)
The End of Time: Part Two - S4-E18
Revealing mistake: When the Doctor is being rolled down the stairs whilst he is strapped to the chair, it is apparent that in the wide shots, it is a dummy in the chair and not the Doctor. In the wide shots, the Doctor is sitting virtually still and motionless, but in the closer shots, he is fidgiting.
The Family of Blood (2) - S3-E9
Revealing mistake: The pyrotechnic mortars used in the destruction of the Family's ship are visible in the shots leading up to their detonation. As the Family run from their ship through the field, the mortars are visible against the branches behind them. Shortly afterwards, they detonate, creating the illusion that the invisible craft has exploded.
Revealing mistake: When the TARDIS dematerialises and causes wind to blow against Churchill and Amy, their clothes are affected - but the cigar smoke in the air is unaffected, and actually drifts towards the vanishing TARDIS. (00:14:25)
Revealing mistake: The Cyber-Leader has a clear section in the top of its head through which its brain can be seen. The brain in question is very obviously plastic.
Revealing mistake: Despite having three suns, everything on Desolation only casts one shadow.
The Pyramid at the End of the World - S10-E8
Revealing mistake: The Monks show the Doctor and company simulations of a future, lifeless Earth - but some visible trees reveal the origins of the footage as being from the aftermath of natural disasters. (00:24:10)
Revealing mistake: When the Doctor fires a champagne cork into Auton-Mickey's head, the lack of spraying or leaking wine, even when the Doctor is seen holding the open bottle horizontally immediately afterwards, makes it quite clear that the champagne bottle is actually empty. (00:25:23)
The Husbands of River Song - S9-E14
Revealing mistake: When Hydroflax's head is sitting on the section of the TARDIS console with the telepathic circuits, the console is obviously sagging inward, as if made of rubber.
The Day of the Doctor - S7-E16
Revealing mistake: When Osgood tells Kate that they're using Derren Brown as the explanation for flying the TARDIS into Trafalgar Square by helicopter, the two women are standing in front of the TARDIS. Its door is slightly open, revealing an interior that is obviously a picture. (00:05:00)
Revealing mistake: Mels is shot in the stomach by Hitler, leading to her regeneration. Rory, when checking the wound, says he's going to try and stop the bleeding. However, when she stands up while glowing with regeneration energy, and in every scene afterwards where Mels/River is wearing that dress, there is no bullet hole or bloodstain visible.
Silence in the Library (1) - S4-E8
Revealing mistake: Also applying to the second episode of the two-parter, "Forest of the Dead": The keyboards on the Library's computer terminals are very obviously standard Apple keyboards - this in an episode set in the 52nd century.
Revealing mistake: When Lilith bespells Shakespeare to write the end of Love's Labour's Won the way the Carrionites want it, there are several shots where a white fleck of some kind is visible in the lower centre of the screen, stuck to the camera lens. (00:17:10)
Revealing mistake: In the museum after the Doctor, Amy, young Amy and Rory escape the Stone Dalek, the Doctor uses the Vortex Manipulator to go back in time to tell Rory in 102 AD to let him out of the Pandorica. The third time he goes back, Amy moves despite being dead. (00:19:38)
Revealing mistake: In the underground scene in the Nestene lair, the CGI used to create the Nestene is horrendous. And in a shot from behind the Doctor, the Nestene looks like a whole bunch of orange pixels.
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.