Continuity mistake: As the scarecrow-soldiers advance on the school to do battle, the scene cuts to Sister of Mine, looking out from a school window. There is heavy rainfall outside. When we immediately cut back to the advancing scarecrows, it is a cold, clear night. (00:10:00)
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)
Continuity mistake: When Lawrence is watching the Weeping Angel, just after seeing the Doctor's film/Easter egg, he turns away for a split second. By the time he turns back, you see the Weeping Angel's face only inches from Lawrence's face. But you then cut to a wide shot where you see the Angel's arms outstretched, so its face is about half a metre away from Lawrence's face. (00:34:45)
Factual error: A reflection of a full Moon is shown near the end. When Earth is viewed from the Moon earlier, over half of it is illuminated by the Sun. For it to be full Moon, the entire Earth would have to be dark. In addition, the place where the hospital was transported to was dark, and not sunlit. (00:37:45)
Continuity mistake: In the scene when Donna asks the woman if she could borrow £10 because it's Christmas, you can see that Donna is wearing sports shoes instead of her usual white wedding shoes. (00:10:05)
Continuity mistake: When the Master stands up on the Valiant to announce that he is the Toclafane's "Master", President Winters is visible in the background, only the Toclafane aren't there. In the next shot, they return, buzzing around Winters' head.
Character mistake: When the Doctor is taking Donna to 4.6 billion BC to watch the formation of the Earth, he says that it is the furthest back the TARDIS has ever been. But in the 5th Doctor episode "Castrovalva", the TARDIS drifted to 13.2 billion BC and the formation of the galaxy. (00:40:35)
Audio problem: While Billy Shipton is showing Sally Sparrow the TARDIS (in the room where he keeps the abandoned cars), just after he says, '[You] can't even get in it', he rattles the TARDIS' handle to demonstrate. Watch carefully: When he shakes the handle we hear a rattling noise as if the door is shaking, but in fact the door stays rock solid. (00:19:35)
Plot hole: Martha tells the kidnapping couple to switch off all their engines so the Macra don't notice them. Yet during this scene, the car remains hovering above ground, meaning the engines must be engaged in some way, and the Macra should still hear them. And these things don't hover when deactivated - the car was shown to be parked on the ground at the start of the episode.