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.
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.
Continuity mistake: When Lawrence is watching the weeping angel, just after seeing the Doctor's film/easter egg, he turnes away for a split second. By the time he turns back, you see the weeping angel's face only inches from Lawrence's face. Yet, you then cut to a wide shot were you see the angel's arms outstretched, so its face is about half a metre away from Lawrence's face.
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 Earth Formation, he says that it is the furthest back the TARDIS has ever been. But in the 5th Doctor episode "Castrovalva" the TARDIS drifts to 13.2 billion BC and the formation of the galaxy.
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.
Audio problem: When the Doctor and Martha are watching Shakespeare in the Globe, Martha says "He's a bit different to his portraits". After she says this on the left of the screen the Doctor's head comes into shot and you can clearly see by his facial expressions he is saying something to Martha, yet no sound is heard.