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)
The Bells of Saint John - S7-E8
Visible crew/equipment: When on the motorbike, the camera vehicle and equipment is reflected on the Doctor's helmet.
Flux: Chapter One - The Halloween Apocalypse - S13-E1
Continuity mistake: Karvanista smashes his way into Dan's house by breaking down his door with an axe. When the Doctor and Yaz arrive after Dan's abduction, the hole in the damaged door is smaller than it was originally. (00:17:30)
The Sound of Drums (2) - S3-E12
Continuity mistake: In the conference room, Saxon (The Master) puts on a gas mask that has an emblem mounted above the hose. After replying to the question, he moves the mask, and the emblem is on the bottom of the mask.
Revealing mistake: When Robin Hood comes up behind the Doctor to push him into the water, it's obviously a stunt double with a bad wig.
Continuity mistake: The Doctor's hair changes from the time he realises Rory is there to when the Pandorica is unlocking.
The Impossible Astronaut - S6-E2
Audio problem: When the Doctor sits in the Oval Office chair, Secret Service Agents aim their revolvers at him. As they do, the sound of a pistol slide racking is heard. None of them are doing anything except raising and aiming their revolvers at him.
Vincent and the Doctor - S5-E10
Continuity mistake: Amy's tights appear to be gone when she's watching Vincent paint the church. Previously whilst walking to the church they are on.
Continuity mistake: After Missy hooks Clara up to the Dalek armour, she takes her hands away from Clara's temples. However, in shots facing her for the next several shots until she stands up and backs away, her arms are still raised. (00:22:24)
The Magician's Apprentice - S9-E2
Continuity mistake: During the exchange where the Doctor says "You flatter me" and Davros responds "A pity. I intended to accuse", Davros' hand goes from just under his chin to resting on his chair's control panel. (00:40:15)
Continuity mistake: When the Doctor hands out of the base manuals to the expedition crew for the dream test, Albert Smith is shown with his manual open in shots from behind him several shots before he's shown opening it in a shot facing him. (00:35:56)
Factual error: At the end, when the Doctor shows her companions the asteroid named for Rosa Parks, it's depicted in a dense asteroid field which looks absolutely nothing like the (very sparse) asteroid belt does in real life.
Dark Water - S8-E11
Continuity mistake: When it's revealed that the dream patch is on Clara's hand, it's in her right palm. But in the wide shot when she's getting up as the Doctor explains the true nature of the patches, it's on her left hand instead. (00:13:21)
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.