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)
Factual error: When the Immortality Gate is activated, there's a wide shot of Earth as the wave from the device goes around the planet. In another instance of a mistake made by a few previous Christmas specials, despite this taking place on Christmas Day, the North Pole is looking very, very sunny for what's supposed to be the dead of winter. (00:54:50)
Factual error: The establishing shot of Bedlam Hospital shows it with 18th-century neoclassical architecture, in an episode set in 1599, in the Elizabethan era. (00:23:20)
Revealing mistake: There are some moments during the scene where the Doctor is being strangled by the Auton arm where it's fairly obvious that Christopher Eccleston is holding the arm to his own throat. Namely, the moments where the hand isn't quite in the right position, slipping towards his chin.
Continuity mistake: When the Doctor pulls the arm off the Auton and tosses it to Rose, the arm is bent at the elbow and solid plastic, with a smooth, clean break. Later, particularly noticeable when Rose has left the department store, the arm is hollow, with an unbent elbow and a jagged break. The arm continues to change between the two appearances for the rest of its screentime. (00:07:08)
Continuity mistake: When Sally Sparrow is about to take the key from the weeping angel, at first the key is on a piece of string, and that string is wrapped around the weeping angel's left hand. In the next shot, and when she pulls the key out, the string is now only in the angel's palm. (00:10:30 - 00:11:10)
The Woman Who Fell to Earth - S11-E2
Deliberate mistake: The Doctor (Jodie Whittaker) is shown wearing the same clothes that the previous incarnation (Peter Capaldi) wore after regenerating. Peter Capaldi is 6' and Jodie Whittaker is 5'6", but the clothes fit perfectly. She even says her legs used to be longer, and yet the trousers aren't flapping around her feet.
Continuity mistake: The meteors are shown approaching and hitting the ship on the starboard (right) side. Twice, however, they are erroneously described as being to port (left): When the meteors are first seen on the scanner by Frame, and later when Frame tells the survivors in Kitchen 5 to go starboard because the port side of the ship is impassable.