Continuity mistake: When Bonnie gets a video call from the Doctor, her grip on the phone changes between shots.
Continuity mistake: For most of the robbery sequence at the beginning, the Nightmare (a disguised Ashildr) is holding her pistol in her right hand. When she's yelling at the Doctor for interfering with her robbery while he's looking at the chest strapped to the back of the carriage, however, she's holding it in her left hand. It switches back to her right after the carriage escapes.
Deliberate mistake: In real life, Viking helmets didn't have horns on them, because it would be a liability in combat. The horns were actually for drinking. The Vikings in this episode were given horns anyway, because the writers didn't feel it was worth having to include an explanation of hornless helmets to a general audience.
Continuity mistake: When the Doctor is listing questions about what exactly the ghosts are, he goes from gesturing with his left hand in the close-up to gesturing with his right in the wide shot. (00:17:17)
Audio problem: Shortly after arriving at the Drum and taking shelter in the Faraday cage, when the Doctor is looking out the window in the door at the ghosts, he says "What are you?" His jaw doesn't move.
Continuity mistake: Missy's cameo brooch is unpinned and hanging askew when she vaporizes Osgood, but the brooch rights itself and is pinned properly when Missy steps on Osgood's eyeglasses. (00:23:00)
In the Forest of the Night - S8-E10
Continuity mistake: When Clara is looking at the drawing in Maebh's homework book while the Doctor tells her about the solar flare, her grip on the book changes between shots. (00:22:44)
Continuity mistake: During the early scene with the Cybermen outside St Paul's, when Missy pulls out her phone/disintegrator weapon and shows the Doctor pictures of the Cybermen going viral all over the planet, and when she prepares to take a picture of the two of them, her grip on the device, as well as which hand she's holding it in, keeps changing between shots. (00:03:00)
Continuity mistake: When Missy orders her Cybermen to blow up the plane and kill some Belgians, her control bracelet is missing from her wrist in one shot. (00:33:54)
Mummy on the Orient Express - S8-E8
Continuity mistake: When the Doctor phones Clara and discovers she's trapped in the locked car with Maisie, his phone keeps switching hands. (00:21:55)
Factual error: After PC Forrest is killed by the Boneless, her nervous system is flattened and displayed on the wall, appearing as a mural. However, there are far too many nerves around where her liver would have been and not nearly enough around her brain.
Continuity mistake: When Courtney comes into The Caretaker's room in search of paper towels, there is a "keep out" sign (reading "Go Away Humans") hanging in the window of the inner door. When the Doctor is talking to her just before she leaves, the sign is missing. Over the course of the rest of the episode, the sign proceeds to appear and disappear a few more times. (00:15:50)
Time Heist - S8-E5
Continuity mistake: Near the end, when the Doctor and Clara are standing by the TARDIS on the planet they took the Teller and its mate to, Clara's hands go from touching the buttons on her jacket to loosely clasped lower down. In the third shot of her, they return to the first position. (00:44:28)
Revealing mistake: During the sequence where the Cyber-clouds covering Earth are burned away, there is a shot showing the clouds burning over the Sydney Opera House. The shot is, very obviously, a still image to which CGI of the burning sky has been added, with extremely unconvincing results. (00:47:37)
The Day of the Doctor - S7-E16
Continuity mistake: After Clara enters the Doctors' cell, and they're talking about how the door was unlocked, shots inside the cell show the door about halfway closed, while a shot from outside looking into the cell shows the door wide open. (00:45:25)
The Day of the Doctor - S7-E16
Continuity mistake: During the scene in the barn where the three Doctors have their hands on the button, when Eleven notices Clara crying and asks her what's wrong, the Doctors' hands go from stacked on top of each other on the button to only touching it with their fingers. (01:02:40)
The Name of the Doctor - S7-E15
Continuity mistake: When the Doctor is talking to River just before entering his own timeline to rescue Clara, in the shots facing him, the glowing column representing his timeline is not visible, despite the fact that a wide shot reveals he's standing right in front of it. (00:39:25 - 00:40:04)
Factual error: During the chase on the motorway, many deciduous trees sporting lush green leaves can be seen in the background, in sharp defiance of the fact that it's supposed to be Christmas Eve and their branches should be bare. In addition, despite having chosen to wear a sleeveless wedding dress, Donna is remarkably unbothered by the fact that it should be fairly brisk outside, probably somewhere around freezing.
Journey to the Centre of the TARDIS - S7-E12
Continuity mistake: When the Doctor is asking Clara if she feels safe in the last scene, most of her hair is draped over her left shoulder. However, whether some of her hair is draped over her right shoulder or not changes between shots. (00:45:05)
Other mistake: When Mr. Thursday goes to see Vastra, to hire her to investigate his brother's death, he doesn't see her face (she's a Silurian "lizard woman from the dawn of time") until she lifts her veil to take a closer look at a photograph he brought her, upon which he faints. However, Vastra's veil is quite see-through, enough that her non-human appearance is obvious to the audience even before she lifts it. The same thing happens when she goes to visit the coroner later - although he doesn't faint.
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.