Factual error: Magnetic tape recorders weren't available outside of Germany during World War II. True the tape recorder could have been captured from the Germans, but, as it was "cutting edge" technology for 1941, it would hardly be likely to have ended up in a hospital office.
Factual error: One of the programs on the new television set is "Animal, Vegetable, Mineral?". In 1953 this quiz show was broadcast on Thursdays. But, it's the eve of the coronation, which makes it Monday the 1st of June. "Animal, vegetable, mineral?" wasn't on that evening.
Factual error: In the opening shot of this episode, we see the Earth from space. The camera then zooms into Western Europe, the UK, London, then into Rose Tyler's flat, where a jump cut to an alarm clock shows its 7:30am. But look again at the start of that sequence: it shows that it's daylight over the UK - and over the USA. This is of course impossible. When it is 7:30am in London, it is 2:30am in New York, as Eastern Time is 5 hours behind UK time. Usually, in New York, at 2:30am it is not daylight because it is the middle of the night.
Factual error: Ida, the science officer, says that the planet is in geostationary orbit around the black hole. However, the word "geostationary" applies very specifically to objects orbiting the planet Earth. Since a black hole is a type of star, this planet's orbit could be described as astrostationary, or even just stationary, but definitely not as geostationary. A science expert on an interstellar mission wouldn't make this mistake, and she wasn't dumbing things down, either, since "geostationary orbit" is already a pretty obscure topic for people unfamiliar with space technology.
Factual error: When Rose is locked in the room and the bodies come toward her, you can see a modern-day electric light-switch to the side of the door she's trying to get through. As the Doctor runs down the hall toward her, you can see a central heating radiator. Both are wildly anachronistic for the time period.
Factual error: Emergency Service vehicles in Cardiff (indeed, throughout Wales) have their signs in bilingual English/Welsh. So the Police cars and Ambulances seen in this episode should have 'Heddlu'/'Police' and 'Ambwlance'/'Ambulance' bilingual logos. However all the Police Cars and Ambulances seen in this episode have their logos in English only.
Factual error: When the Doctor spots Rory taking a photo of Prisoner Zero, we're shown a brief close-up of Rory's hospital identity badge. The date of issue is given as "30/11/1990". The main body of the episode is set in 2008, two years before Rory and Amy's wedding in 2010. It's further established in the episode that Rory and Amy played together as children after her first meeting with the Doctor in 1996, with Rory observing that Amy made him dress up as the Raggedy Doctor. Rory could not possibly have worked for the hospital for eighteen years at the time of the episode.
Factual error: The army shoot at Martha's car and you can see sparks where the bullets bounce off her windscreen. But, at that close range, one of those things can go through a brick! I know you're supposed to allow a bit of disbelief, but this is taking it too far.
Factual error: When Rose gets the message there are two things wrong with what you see on the phones screen: firstly on the top right of the screen you can see the icon for mute even though you heard the beep, and secondly that screen is for when you type in the number you want to call (text), not the screen for receiving a text.
Factual error: Look closely at some of the freight wagons at 'Limehouse Green' railway station: several of them appear to have 'British Rail Freightliner' livery. This episode is set in 1941, but British Rail did not exist until 1948, and the Freightliner Division did not exist until the 1980s.
Factual error: The rank insignia of the Soviet officers is completely inaccurate. The captain wears the epaulets of a captain first rank (captain) and the sleeve insignia of a captain second rank (commander). Lieutenant Stephashin wears the epaulets of a senior lieutenant and the sleeve insignia of a captain third rank (lieutenant-commander). The third officer wears the epaulets of a captain second rank and the sleeve insignia of a captain third rank.
Factual error: A reflection of a full moon is shown at the end. But when Earth is viewed from the moon, half of it is in the light. For a full moon to take place, most of the Earth would have to be dark.
Factual error: In this episode, it is stated that the Moon's sudden increase in mass caused a devastating global high tide. The amount of the increase in mass is given as 1.3 billion tonnes. But the Moon has a mass of over 70,000,000,000 billion tonnes, or over 50 billion times the supposed increase. Such a negligible increase in mass, less than.000000002%, would have almost no effect on Earth's tides, let alone be devastating.
Factual error: Near the end of the episode, the full moon is shown in the daytime sky, well above the horizon. This is impossible, as any celestial body lit by the Sun has its full phase only when it is directly opposite the Sun; thus, a full Moon rises at sunset and sits high in the sky only during the night. For the Moon to be in the sky during the day as shown, it would have to be visibly of a phase other than full.
Factual error: When The Doctor, Amy and Rory are on the roof and the Doctor says "The question for now is total event collapse means that every star in the universe never happened", the Gherkin can be seen in the background. However, the Gherkin wasn't built until 2003, where as this episode takes place in 1996.
Factual error: The Doctor (and the staff on the station) refer to the idea of a planet being in orbit around a black hole as 'impossible'. It is not. Gravity (and physics in general) works perfectly well outside of the event horizon. For all practical purposes - regarding orbiting around it - the black hole might as well be any other object, as long as it has an equal mass.
Factual error: Clara determines the location of the enemy's base of operations: floor 65 of The Shard. However, there are multiple issues with this conclusion. Firstly, floor 65 is a residential property, not an office location; offices in The Shard occupy floors 2 through 28. Secondly, the view of 30 St Mary Axe from Miss Kizlet's window puts the office below 180m, the height of the latter building. This would mean the office must be below floor 50. Finally, when The Doctor rides his motorcycle up the side of the building, 30 St Mary Axe is again seen, this time significantly below his location, and on the wrong side of The Shard. Not only then does the office's height change, but also which side of The Shard it is on.