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 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)
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)
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.
Continuity mistake: The meteors are shown approaching and hitting the ship on the starboard (right) side. Twice, however, they are erroneously described as being to port (left): When the meteors are first seen on the scanner by Frame, and later when Frame tells the survivors in Kitchen 5 to go starboard because the port side of the ship is impassable.
Revealing mistake: When the Editor activates the Doctor and Rose's manacles, the right manacle binding Rose's wrist snaps open as they are shocked. (00:35:12)
Continuity mistake: When Sarah Jane is talking to Rose while she's trying to access a computer in the lab, half-sitting on the desk, the right side of Sarah's jacket is bunched up beneath her arm in shots facing her and lying down in shots facing Rose.
Continuity mistake: During the opening montage, showing the Slitheen incapacitated by electrocution, when Margaret drops Indra's body and stumbles back, a close-up of the body on the floor shows her legs without the pulsing electricity covering her entire body, which is visible in other shots.
Continuity mistake: When Harriet Jones is hiding in the closet and spying on the Slitheen attacking General Asquith, wide shots of the closet door have it in shadow, but close-ups of Harriet have the part of her face that is visible illuminated.
The Wedding of River Song - S6-E14
Other mistake: When the Doctor walks into the control room at the base, the time on the computer is frozen between 5:02:57pm and 5:02:58pm. The Doctor grabs River's hand, and time begins moving up to 5:03:00pm before he is restrained. Later, when the Doctor and River kiss and time begins moving again, the time is 5:02:00pm.
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.
Flux: Chapter Three - Once, Upon Time - S13-E3
Continuity mistake: In the previous episode Swarm put markings on Yaz and Vinder to mark them as replacement Mouri but in this episode, which takes place right after, they no longer have any markings.
Other mistake: When the Doctor gets George's psychic cry for help, he's shown reading the message without opening the wallet containing the psychic paper. This despite the fact that all previous instances of the Doctor receiving psychic messages this way has required him to open the wallet, suggesting that the wallet itself does not display the message. (00:02:02)
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.