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.
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, which can be seen 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 yet Xiaolian is still standing in the same spot in the shot facing the Monk.
Continuity mistake: When the Doctor and Nardole are being held by the Picts in a circle of weapons being pointed at them, when Kar's brother points a knife at the Doctor and warns him not to speak until she gets back, his arm is almost fully extended in shots from above and facing the Doctor, but much more bent in shots facing him.
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.
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.
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.
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.
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.