The Pyramid at the End of the World - S10-E8
Factual error: The American officer is called a Colonel but he wears the four star rank patch of a General, and that rank patch is even upside down in some scenes. The stars should have one point upwards.
The Pyramid at the End of the World - S10-E8
Continuity mistake: While the Doctor, et al. Are in the pyramid with the Monks, when the Monk tells the Secretary General that if his consent isn't pure it will kill him, Xiaolian is standing right behind him in shots facing the Secretary General and shots facing the Monk, but in the one shot of the Secretary General as he's being vaporized Xiaolian has vanished, but Xiaolian is still standing in the same spot in the shot facing the Monk. (00:26:10)
The Pyramid at the End of the World - S10-E8
Visible crew/equipment: Right before the TARDIS materializes in the lab at Agrofuel, there's an overhead shot of Erica at the desk, and the two green tape X marks on the floor behind her are visible, precisely where Douglas had collapsed and his white protective gear should be. Note there's an earlier overhead shot of the same area before the incident, when Erica brings Douglas the coffee, and those tape marks are not there. (00:32:50)
The Impossible Planet (1) - S2-E11
Factual error: The graphics depicting the black hole show matter falling directly towards the centre of it. This would only happen if all the matter happened to be heading in that direction already. In reality, matter approaching the black hole at any other angle would swirl around the event horizon, like water going down a plughole.
Character mistake: When Rose thinks Mickey is dead, she says she'll have to tell his mother. But in Rise of the Cybermen in Series 2, she says that Mickey's mother has been dead since he was a child.
The Impossible Planet (1) - S2-E11
Other mistake: When the Doctor asks what the planet is called, Ida says, 'Don't be stupid, it hasn't got a name, how could it have a name?' A few minutes later, she tells the Doctor the planet is called 'Krop Tor'.
Plot hole: Martha tells the kidnapping couple to switch off all their engines so the Macra don't notice them. Yet during this scene, the car remains hovering above ground, meaning the engines must be engaged in some way, and the Macra should still hear them. And these things don't hover when deactivated - the car was shown to be parked on the ground at the start of the episode.
Character mistake: When the news broadcast on the destruction of Henrik's is shown, the chyron misspells the store's name as "Henrick's." (00:07:50)
Character mistake: Dr Singh refers to "a single protozoa." "Protozoa" is the plural form. He ought to have said "a single protozoan." (00:08:05)
Character mistake: The Doctor gets excited about the major events of 1953 and mentions that everything was "off the ration" (that is, the food rationing put in place in the UK during the Second World War had ended). Rationing actually ended the following year. (00:05:55)
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)
Utopia (1) - S3-E11
Continuity mistake: When the Doctor gets the rocket to work by tinkering with the boost reversal circuit, he picks it up with his left hand, sonics it, and then transfers it to his right hand, all in a shot where he has his back to the camera. In the next shot, facing him, he's holding it in his left hand as he pulls something off the device. The shot after that, facing Professor Yana again, the circuit is back in his right hand. (00:18:50)
Utopia (1) - S3-E11
Character mistake: When the Futurekind spy starts sabotaging the silo's systems, and Chantho notes that they're losing power, she says, "We're losing power-tho!" - forgetting the "Chan-" prefix that she starts anything she says with, in order to not swear by her species' standards. (00:27:00)
Continuity mistake: When Clara takes Rigsy's chronolock, in the closeup of the tattoo Clara's lifting her hair with her right hand and showing the tattoo with her left hand, but in the next front-facing shot her hands have switched, she's holding up her hair with her left hand and showing the tattoo with her right hand. (00:26:45)
Continuity mistake: At the beginning, Missy is using a knife to sharpen a stick to a point. Later in the scene, when she says to Clara that if they go rescue the Doctor, everything the Daleks can throw at them is between them and him, she lists only the stick among their assets. The knife is never seen or mentioned again after Missy was done with it. (00:04:18)
Factual error: The Koh-i-Noor, as depicted in this episode, looks absolutely nothing like the real diamond. The episode's gemstone is about the size of the palm of the Doctor's hand, and shaped in a stereotypical brilliant cut. The real Koh-i-Noor is much smaller and oval-shaped.
Factual error: When the Immortality Gate is activated, there's a wide shot of Earth as the wave from the device goes around the planet. In another instance of a mistake made by a few previous Christmas specials, despite this taking place on Christmas Day, the North Pole is looking very, very sunny for what's supposed to be the dead of winter. (00:54:50)
Factual error: The establishing shot of Bedlam Hospital shows it with 18th-century neoclassical architecture, in an episode set in 1599, in the Elizabethan era. (00:23:20)
Revealing mistake: There are some moments during the scene where the Doctor is being strangled by the Auton arm where it's fairly obvious that Christopher Eccleston is holding the arm to his own throat. Namely, the moments where the hand isn't quite in the right position, slipping towards his chin.
The Woman Who Fell to Earth - S11-E2
Deliberate mistake: The Doctor (Jodie Whittaker) is shown wearing the same clothes that the previous incarnation (Peter Capaldi) wore after regenerating. Peter Capaldi is 6' and Jodie Whittaker is 5'6", but the clothes fit perfectly. She even says her legs used to be longer, and yet the trousers aren't flapping around her feet.
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.