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)
Revealing mistake: When the Doctor travels back in time after being shot by the stone Dalek, falls down the stairs and tells himself that he has 12 minutes to live we never see either of the 2 Doctors' faces onscreen at the same time, and if you look at the hair on the Doctor that's dying it is completely different to Matt Smith's. That's because it is Gordon Seed, Matt Smith's stunt double.
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)
Plot hole: Those people created for medical experiments cannot run. In fact they can barely walk, so how come they can climb nearly as fast as Rose? What's more, when you see them climbing, they seem to have little ability to coordinate hand over hand. Even with the delay brought on by the cat-woman-thing, they should not have been able to keep up with her.
Revealing mistake: When the alien spacecraft crashes into Big Ben, it is obvious that the shot has been reversed/flipped around. Look at the Roman numerals on Big Ben's clock face: They should read (clockwise from the top) XII, I, II, III, and so. Instead they read IIX, IX, X, etc. (00:06:35)
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)
Visible crew/equipment: After Miss Kizlet enters her office to find the walking base station Doctor sitting at her desk, as she walks around the motorbike lying on the broken glass, when this 'Doctor' says, "Yes, those still with bodies to go home to would be free," we can see the moving reflection of two crew members on the surface of the motorbike.
Continuity mistake: When the Doctor and Clara are on the rooftop terrace, there's a distinctive design on the Doctor's bow tie, but when he's in the coffee shop the bow tie's design differs, and when he runs outside to ask if Clara's okay it changes back, then it changes again when he's in back the shop. Additionally, when the walking base station Doctor uploads Clara it's wearing a bow tie, and its design also changes on the motorbike and in Kizlet's office.
Continuity mistake: After Strax hits Clara with a newspaper she comes downstairs and he asks her if she needs anything. She asks for water and he places the bucket of mop water on the table in front of Clara. They have a conversation about the water and at the end of the conversation Clara looks at her newspaper and the bucket has disappeared from the table in front of her. Neither of them moved it. (00:26:45)