Revealing mistake: When the Doctor and Rose are talking at the bay, the Doctor's hair is blowing in the wind, but it's not when he is shown in the TARDIS. Considering the image of him on the beach is a projection of him in the TARDIS, the two versions should match. The actor was obviously on the beach recording his lines with Rose and back on a set doing the inside scenes.
Continuity mistake: When Mickey enters one of the school's computer rooms, dozens of pupils are busy typing, and every one of them is also wearing headphones. However, once Mickey unplugs the main connection for the computers, and shouts for the students to leave, when the students begin to get up, their headphones have instantly removed themselves from their heads and been placed neatly on the desks next to the computer keyboards. (00:36:25)
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.
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.
Continuity mistake: At the end of the episode, Donna piles suitcases in the Doctor's arms in preparation to leave with him in the TARDIS, and places a striped hat box on top. The bags stay that way for a while as the camera cuts back and forth between them, and you can see the stack of luggage as the camera films the Doctor from behind. Then, as soon as the camera cuts back to the Doctor's face when Donna leaves to give her mother the car keys, suddenly he has one bag under his arm and another in his hand, and the rest of the bags are on the ground with the hat box stacked neatly on top. In addition, when the scene cuts from Donna closing the hatch of her car to her and the Doctor standing by the TARDIS, a large floral-patterned suitcase has appeared, which she was not shown removing from the vehicle. (00:43:15)
Other mistake: After the Doctor tells Bill that Heather's face isn't symmetrical, when he and Bill look into the "puddle" together the Doctor explains that instead of seeing her normal backwards reflection, she's seeing her face "the right way round." The problem occurs in the next shot of the Doctor and Bill seen in the puddle, because the "WOW!" patch on Bill's jacket is properly where it should be, but note everything else is actually backwards. Things such as Bill's color-block top and her denim jacket buttons are on the opposite way. Also note the Doctor's ring has switched hands. Presumably this shot was edited, and the "WOW!" patch was blurred on the left of Bill's jacket then digitally added to the right side, to give the appearance that it's "the right way round" as the Doctor said. (00:20:15)Super Grover
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)
Deliberate mistake: When the Doctor visits all his recent companions before he regenerates, he goes to a book signing of A Journal of Impossible Things, written by Joan Redfern's great-granddaughter. When she is signing the book for the Doctor, you can hear the scratching effect from the pen but you can see that the pen isn't touching the paper. (00:59:50)Professor Lazarus
Continuity mistake: While the Doctor, et al. are in the pyramid with the Monks, when the Monk tells the Secretary General that if his consent isn't pure it will kill him Xiaolian is standing right behind him, which can be seen in shots facing the Secretary General and shots facing the Monk, but in the one shot of the Secretary General as he's being vaporized Xiaolian has vanished yet Xiaolian is still standing in the same spot in the shot facing the Monk. (00:26:10)Super Grover
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 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.