Character mistake: When the Futurekind spy starts sabotaging the silo's systems, and Chantho notes that they're losing power, she says, "We're losing power-tho!" - forgetting the "Chan-" prefix that she starts anything she says with, in order to not swear by her species' standards. (00:27:00)
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. (00:32:50)
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: At the beginning, Missy is using a knife to sharpen a stick to a point. Later in the scene, when she says to Clara that if they go rescue the Doctor, everything the Daleks can throw at them is between them and him, she lists only the stick among their assets. The knife is never seen or mentioned again after Missy was done with it. (00:04:18)
Factual error: The Koh-i-Noor, as depicted in this episode, looks absolutely nothing like the real diamond. The episode's gemstone is about the size of the palm of the Doctor's hand, and shaped in a stereotypical brilliant cut. The real Koh-i-Noor is much smaller and oval-shaped.
Factual error: The Viking village has tubs of electric eels in the boathouse, which prove instrumental to the plot as the power source of the makeshift electromagnet used to relieve several of the attacking aliens of their helmets. The problem is that the Vikings live somewhere in northern Europe, and this episode takes place in the 800s. Electric eels are native to the Amazon and Orinoco rivers of South America, which at this point in history no one in Europe knew existed.
Continuity mistake: After the Doctor is knocked unconscious, Clara uses the psychic circuitry to pilot the TARDIS to what turns out to be a moment in the Doctor's past, in the barn first seen in "The Day of the Doctor." The loft in the barn where the young First Doctor is sleeping in bed, however, was not present in the previous episode.
Plot hole: The Doctor leaves Martha a recording with instructions for her for when he's human. However, the flashbacks to the incident that led to him using the Chameleon Arch don't leave enough - or any - time for him to have made the recording, presenting his decision to use the device as a spur-of-the-moment one that he immediately acts upon.
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)