The Vampires of Venice - S5-E6
Factual error: Isabella is a black girl living in 1580 Venice. So how is it that she has perfectly straight hair, when modern hair care products won't be invented for centuries?
The Christmas Invasion - S2-E2
Factual error: The episode kicks off with a reuse of the zoom-in from orbit first seen in "Rose." As the sunny North Pole indicates, the Earth is depicted as if it is the height of Northern Hemisphere summer, even though as the title of the episode indicates, it begins on Christmas Eve, three days after the northern Winter Solstice when the Pole is in darkness. (00:00:05)
Factual error: When the TARDIS is flying over London at the beginning, the London Eye is visible. It's supposed to be 1996, and the Eye was built later than that, for the new millennium celebrations. (00:00:30)
Factual error: The opening shot of the episode reuses the zoom-in from orbit originally used in "Rose." The North Pole is sunlit, as it would be at the height of summer. "The Runaway Bride" takes place on Christmas Eve, four days after the Northern Hemisphere's Winter Solstice, when the Pole would be facing away from the Sun, in darkness. In fact, this was the second Christmas special in a row to make this mistake, after "The Christmas Invasion." (00:00:05)
Factual error: During the climax, the Moon is visible in the background, and is depicted as full. On December 24, 1851 in real life, the Moon was at first quarter phase.
Factual error: The Doctor says that the Earth is six billion years old, which is one and a half billion years over - it's only 4.5 billion years old. (00:21:25)
The Bells of Saint John - S7-E8
Factual error: The view from Ms Kizlet's window was taken somewhere in the vicinity of London Wall eg. the Museum of London, not from The Shard.
Factual error: The Doctor sets the atmosphere on fire, but only the upper part burns. The atmosphere extends from the Earth's surface (where it is densest) upwards, and so the flames would come right down to the ground, burning everyone to death. Of course that wouldn't work with the plot, so artistic licence has been applied.
The Unicorn and the Wasp - S4-E7
Factual error: In Lady Edison's flashback, she's reading "The Murder Of Roger Ackroyd", her favorite book. However, this episode is set in 1926, and the dust cover is from 2006.
Factual error: The all important date of 26/06/2010 and it ticks over on Amy's alarm clock right at the end of the episode. However it shows 11.59 AM and flicks over to midday (12.00PM) the next day. The date should've stayed on 25/6 or, as I suspect was the intention, the clock should've read 11.59 PM and then ticked over to 12.00 AM thus changing the date correctly. (00:41:00)
The Doctor, the Widow and the Wardrobe - S7-E1
Factual error: Cyril is introduced looking at the Moon with a telescope... in a brightly-lit room through a window with the curtains mostly shut, circumstances in which he's not going to see anything at all. (00:03:56)
The Wedding of River Song - S6-E14
Factual error: During the zoom-out from Earth at the end, the Sun is depicted as far, far too large than it actually appears from Earth. (00:40:03)
Factual error: Colonel Mace says the Sontaran ship is orbiting 5,000 miles (8,050 km) above the Earth. However, in shots of and from the ship in both this episode and "The Sontaran Stratagem", the Earth appears far too small for the ship to be that close, with the ship's true distance appearing to be well over double that. (00:08:34)
Factual error: The upper peninsula of Michigan is missing on the map of the US shown on Van Statten's monitor.
Suggested correction: In that era of Doctor Who the Earth was being invaded by aliens on a regular basis. Since the story is set in the 'future' year of 2012, anything may have happened to wipe that part of Michigan off the map.
I'm from Michigan and when I noticed the UP missing, I jokingly said to a friend "looks like Canada stole that finally"
Factual error: By halfway through the episode, the plot is alternating between following Clara and Jac in London, the Doctor in the fictional Central Asian country of "Turmezistan", and Kate in New Mexico. Despite the three locations being scattered all around the world, only in London is it depicted to be nighttime at any point in the episode. Central Asia and the southwestern USA are both shown to be daytime, despite the two locations being over halfway around the world from each other, and the events all taking place at roughly the same time.
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.
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)
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.
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)
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)