Other mistake: When the Earth's nuclear launch sites are being brought online, country by country, in preparation for a strike at the Sontaran ship, Russia is puzzlingly omitted, even though North Korea of all nations is included. (00:17:20)
The Unicorn and the Wasp - S4-E7
Factual error: In real life, Agatha Christie's famous disappearance occurred in December 1926. This episode is quite plainly not set in winter, what with the outdoor garden party and lush green foliage.
Revealing mistake: When Lilith bespells Shakespeare to write the end of Love's Labour's Won the way the Carrionites want it, there are several shots where a white fleck of some kind is visible in the lower centre of the screen, stuck to the camera lens. (00:17:10)
Plot hole: When the Doctor realises that something is coming up from below ground, he tells Nasreen and Tony that at the speed the three transports are coming, the underground arrivals will reach the surface in 12 minutes. The rushed preparations that ensue, including hurrying from the drill hall to the old church and setting up a surveillance network outside, couldn't have taken less than 12 minutes to set up, especially given that they also had to: inform the others trapped inside the shield (Rory, Ambrose and Elliot), inform Rory and Ambrose that their significant others (Amy and Mo) were missing, run between the old church and the block of houses and gather supplies. And, lest we forget, there's also Rory and the Doctor arguing about what happened to Amy and Ambrose's initial skepticism as to what is occurring.
Last of the Time Lords (3) - S3-E13
Factual error: When time is seen rewinding after the destruction of the Paradox Machine, the Earth and Moon are seen rotating and orbiting backwards. The Moon is depicted far closer to Earth than it actually is. (00:37:40)
Plot hole: At the beginning, when the Doctor, Clara, Angie and Artie get off the TARDIS, the two kids are absolutely convinced that they're on the Moon, despite the Doctor explaining that they're actually at the Spacey Zoomer ride on Hedgewick's World, the greatest amusement park in the universe. The kids only realise they really aren't on the Moon when Webley emerges from inside of a fake rock formation, followed by the soldiers. The part of the room that the soldiers come from, which should have been fully visible to the time travellers from the beginning - in fact, they should have been looking directly at it when they leaned out of the TARDIS in the very first shot - looks nothing like the Moon and contains a sign for the Spacey Zoomer ride and a large map of the amusement park. (00:00:01 - 00:00:45)
The End of Time: Part Two - S4-E18
Factual error: The Vinvocci ship is said to be orbiting 100,000 miles above Earth, later refined to 105,000 miles. That's one-third of the distance to the Moon, and the Earth's apparent size from the windows of the ship is far too large for them to be that distance, or even 100,000 kilometres above the Earth's surface. Judging by the Earth's apparent size, the spaceship is actually orbiting 6,000-7,000 kilometres above the planet's surface.
Plot hole: After getting out of the Pyrovile escape pod, the Doctor and Donna start running back to Pompeii. In the process, they are somehow able to outrun what appears to be a pyroclastic flow. Pyroclastic flows can reach speeds of up to 700 kph, and should be impossible for them to outrun. (00:38:15)
The Christmas Invasion - S2-E2
Other mistake: When Rose and Mickey are running across the plaza after being dropped off by a cab, a fence is visible between where they are and where the cab pulled up. It is unlikely to say the least that they would have gotten out of their cab right by a fence and climbed over it. (00:08:45)
Factual error: When the Royal Hope Hospital is transported to the Moon, the area it is in is dark, indicating they are on the side of the Moon not currently facing the Sun. However, in a wide shot of the hospital on the Moon, something that looks like the Sun is visible, something that the illumination of the landscape and the Earth shows cannot be visible. (00:07:40)
Utopia (1) - S3-E11
Other mistake: The stet radiation in the red room is able to disintegrate living beings, with the exception of the immortal Jack. People not going in the room are shown to stay out of the line of the door when it's being opened, lest they be disintegrated. When Jack comes out of the room after having finished in there, the Doctor, telephoning the rocket, is in line with the open door yet remains completely fine. (00:35:15)
Utopia (1) - S3-E11
Other mistake: When Professor Yana shows Martha his pocket watch, which she comes to realise is a Chameleon Arch, she initially finds it familiar from the appearance of the back, and eventually asks him if she can see the front. Before she eventually sees the front of the watch, there is a shot where the front is hidden to the camera, but should be perfectly visible to Martha, just as Yana says "It's old. It's not meant to be." (00:34:40)
Factual error: When Clara is watching the Earth through binoculars in order to see whether people left their lights on or off, the planet is rotating at an impossibly high speed. (00:36:15)
Continuity mistake: After the Doctor and Wilf get off the seniors' bus, they're waving goodbye. In a close-up shot, the Doctor is waving with his right hand, but in a wider shot immediately afterwards, he's switched to his left hand. (00:25:10)
The Day of the Doctor - S7-E16
Plot hole: Among the various contents of the Black Archive are visible several objects that shouldn't be there, because it is impossible for U.N.I.T. to have acquired them. In particular: A detonation pack from "Planet of the Ood", set in the 42nd century, a few thousand years in the future. The Supreme Dalek's shell from "The Stolen Earth"/"Journey's End" - it was shot and killed by Jack Harkness, destroying the shell. The restraint chair from "The End of Time", last seen on the Vinvocci's ship. The makeshift sonic screwdriver built by the alternate Amy from "The Girl Who Waited", since that version of Amy was wiped from existence. A different explosive carried by Gregor Van Baalen in "Journey to the Centre of the TARDIS", which is both set in the future and involves a complicated situation in which the events ended up technically not happening.
The Snowmen - S7-E7
Continuity mistake: As Clara first realises the differences in the TARDIS exterior and interior, she goes to circle the outside, leaving the door open. A second later, it's closed, but open upon her entrance.
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)
Continuity mistake: As the Doctor stares down at young Amy, he takes a perfectly red apple from her and bites it. When the angle changes, and he spits the bite out, the apple has changed to an ordinary red and green one. (00:06:05)
Continuity mistake: Davros' chair has metal parts which go over his shoulders - they are attached to the chair, not Davros. When the Doctor steals Davros' chair they disappear, but when Davros is back in it they have reappeared.
The Angels Take Manhattan - S7-E6
Continuity mistake: As the Doctor explains about the book he's reading, he goes from holding it with one hand to two between angles. (00:07:19)
Suggested correction: Perhaps they didn't see everything and only focused on small things, or they remembered the Futurama episode with an amusement park set on the moon.