Continuity mistake: When Bonnie gets a video call from the Doctor, her grip on the phone changes between shots.
Other mistake: The Doctor says "These are a sort of mark 2, yeah?" The subtitles say "These are a sort of Mach 2, yeah?" (00:17:40)
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: When the Shade leaves Clara and she falls, her body is twisted because of the way her legs are bent with one on top of the other and her arms are out to the side. In the overhead shot of her, her positioning has changed, her body isn't twisted and her arms are more straight down her side.
Heaven Sent - S9-E12
Continuity mistake: When the Doctor is first shown discovering the word "bird" written in the sand on the floor of the teleport chamber, the handwriting changes from being somewhat messy in the wide shot to being perfectly neat in the close-up.
Continuity mistake: Rassilon's gauntlet is supposed to be exactly the same one he had in "The End of Time", but the design has changed. Most noticeably, the user's palm is now uncovered.
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 Return of Doctor Mysterio - S10-E1
Continuity mistake: When the Doctor pulls a glass of water out of his pocket and hands it to Grant, it jumps from his left hand to his right between shots. (00:05:05)
Continuity mistake: When the Doctor starts writing "Time" on the chalkboard during class, the "T" is slanted, but in a following wideshot when he's completed the vertical "TARDIS" the handwriting has changed. (00:08:10)
Other mistake: After the Doctor tells Bill that Heather's face isn't symmetrical, when he and Bill look into the "puddle" together the Doctor explains that instead of seeing her normal backwards reflection, she's seeing her face "the right way round." The problem occurs in the next shot of the Doctor and Bill seen in the puddle, because the "WOW!" patch on Bill's jacket is properly where it should be, but note everything else is actually backwards. Things such as Bill's color-block top and her denim jacket buttons are on the opposite way. Also note the Doctor's ring has switched hands. Presumably this shot was edited, and the "WOW!" patch was blurred on the left of Bill's jacket then digitally added to the right side, to give the appearance that it's "the right way round" as the Doctor said. (00:20:15)
Continuity mistake: After the Doctor tells Bill that nothing gets through the TARDIS doors, when she responds that they're made of wood and have windows, the Doctor's left hand changes position between shots from being apparently by his side to suddenly resting on the door. (00:28:40)
Continuity mistake: When the Doctor holds out his sonic screwdriver for the Dalek to scan, his grip on it changes between shots. (00:42:25)
Continuity mistake: When Bill says to the Doctor, "Do what you gotta do," he raises his hands to her. His hands are closer to Bill's face in shots facing him than shots facing her. (00:48:40)
Continuity mistake: When the Doctor picks up a skull from the bones waiting to be ground into fertilizer, the position of his hands holding it changes between shots facing him and shots looking at the skull. (00:15:10)
Continuity mistake: After the Doctor and Bill are tied up in the tent of explosives, when Lord Sutcliffe pulls out his pocket watch to check the time and notes that the elephant is being brought onto the ice, in a shot facing the Doctor and Bill the watch chain is taut. When the shot cuts to look at Sutcliffe and his henchman, the chain is slack. (00:33:40)
Knock Knock - S10-E5
Continuity mistake: When Bill walks out of the TARDIS, her teddy bear is lying in the box she's carrying with its head to Bill's right. In the next shot from behind Bill as she sets the box down on the ground, the teddy is suddenly lying the opposite way. (00:06:45)
Continuity mistake: During the Doctor's class he draws lines on the chalkboard, which continually change shape between shots. (00:04:05 - 00:05:10)
Visible crew/equipment: When Bill and Nardole run away at the end of the countdown, the reflections of the camera dolly and camera operator are visible on the CERN countdown board. (00:35:55)
The Pyramid at the End of the World - S10-E8
Continuity mistake: When Erica's eyeglasses get smashed, they're seen in a closeup inside her bag and the lens frame is cracked, but when she takes it out of her bag both lens frames are intact around the broken lenses. Also, when Erica takes the eyeglasses out of her bag she holds the eyeglasses' right temple in the closeup, but in the next shot it's the left temple being held up. (00:06:15)
The Pyramid at the End of the World - S10-E8
Continuity mistake: When the Doctor, Bill, Nardole, et al. first see the pyramid their long shadows are cast directly in front of them, but when the Doctor decides to "bring it" and crosses the barrier, their long shadows are cast directly to their right. Then it keeps changing in the following shots when the Doctor approaches the pyramid. (00:10:45)
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.