Character mistake: When the news broadcast on the destruction of Henrik's is shown, the chyron misspells the store's name as "Henrick's." (00:07:50)
Character mistake: Dr Singh refers to "a single protozoa." "Protozoa" is the plural form. He ought to have said "a single protozoan." (00:08:05)
Character mistake: The Doctor gets excited about the major events of 1953 and mentions that everything was "off the ration" (that is, the food rationing put in place in the UK during the Second World War had ended). Rationing actually ended the following year. (00:05:55)
Continuity mistake: After the Doctor steps through the hologram of his past selves and introduces himself to the Atraxi, in a wide shot, there's a red jacket lying on the ground to the left of Rory. In a close-up of Amy and Rory immediately following, the jacket has suddenly leaped into Rory's arms, to join the other clothes he's holding. When the Atraxi flies away, the red jacket is back on the ground again. (00:53:55)
Utopia (1) - S3-E11
Continuity mistake: When the Doctor gets the rocket to work by tinkering with the boost reversal circuit, he picks it up with his left hand, sonics it, and then transfers it to his right hand, all in a shot where he has his back to the camera. In the next shot, facing him, he's holding it in his left hand as he pulls something off the device. The shot after that, facing Professor Yana again, the circuit is back in his right hand. (00:18:50)
Utopia (1) - S3-E11
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)
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.
Suggested correction: These events take place thousands of years apart. Buildings (especially wooden ones) are likely to change in that time.
The barn appears three times, in "The Day of the Doctor", "Listen" and "Hell Bent." Its appearance in "The Day of the Doctor" is chronologically in-between its appearances in "Listen" and "Hell Bent." Both of the two latter episodes have the loft, but "The Day of the Doctor" doesn't. That's the mistake here.
The Time of Angels (1) - S5-E4
Character mistake: When Amy says "Doesn't anybody need me?" from the door of the dropship, there's a misspelling on the door: "Trip Hazzard" instead of "Trip Hazard." (00:16:19)
Daleks in Manhattan (1) - S3-E4
Continuity mistake: When Diagoras enters the Daleks' lab, he is shown pulling on his right glove twice. (00:18:55)
Revealing mistake: In close-ups of the modified pig, seams are visible on its forelimbs. (00:22:45)
Continuity mistake: When little Amy looks out the window to see what makes the noise, you can see the TARDIS through her window (it's a little blurry) but when you look through the window properly, it isn't there.
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)
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)
Silence in the Library (1) - S4-E8
Visible crew/equipment: While the Doctor tries to get into the data core (after Proper Dave tried) it cuts to the telephone still ringing, and when the young girl asks her dad why he's not answering the phone, just as he tells her that the phone is not ringing the boom mic dips into view at the top of the screen. (00:19:40)
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)
Other mistake: O'Donnell imitates another character retching. The subtitles show this as (WRETCHES). (00:03:00)