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. (00:07:15 - 00:08:30)
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: 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: The graphics depicting the black hole show matter falling directly towards the centre of it. This would only happen if all the matter happened to be heading in that direction already. In reality, matter approaching the black hole at any other angle would swirl around the event horizon, like water going down a plughole.
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 it's 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. In New York at 2:30am it is not daylight, because it is the middle of the night. In addition, later episodes make it clear this episode is set in March. The North Pole is fully sunlit, which it never is in March, due to the equinox that happens that month. (00:00:50 - 00:02:00)
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. (00:33:10)
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. (00:07:40)
Factual error: When introducing himself to the Toclafane, President Winters refers to himself as "President-elect of the United States of America." President-elect is the title given to the victor of an American presidential election who has not yet been sworn in, between early November and January 20. This was a mistake on Russell T Davies' part, as he was under the impression it was a longer, formal title for the American president. (00:37:40)
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. When the Doctor hears her screaming for help and runs for her, you can see a central heating radiator. In fact, the undertaker's house has at least two radiators in different hallways. Both are wildly anachronistic for the time period. (00:16:30 - 00:17:08)
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, the police car seen after the earthquake has its label in Welsh only. (00:40:33)
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: When the Doctor regrows his hand during the swordfight, he says that he can do this because he's still within the first 15 hours of his regeneration cycle, and there's still residual energy in his body. However: In both this scene, and the episode's opening scene, when the TARDIS arrives in London, it is full daylight. The episode takes place on Christmas Eve and Christmas Day, 3-4 days after the Winter Solstice. London, at 51°N latitude, has a night longer than 15 hours at that time of year, meaning the Doctor should have been out of luck.