Revealing mistake: Dalek is escaping and enters the large room with the soldiers. He starts the sprinklers so he can kill them faster. When they show the dead soldiers they show some casings which were ejected from the soldiers' guns. The casings still have projectiles in them. If used, they would have been in magazines and would never fall out like they are shown.
Revealing mistake: The Doctor and Rose locate the "metal" hatch that leads down into the "Plastic's Leader" blob. Watch carefully after the Doctor removes the "metal" hatch and moves it aside. The entire hatch "pops-up" a second later. This is because it is plastic and it was suctioned to the floor.
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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 Bens's clock face: They should read (clockwise from the top) XII, I, II, III, and so. Instead they read IIX, IX, X, etc.
Revealing mistake: The 'earthquake' that takes place in this episode results in CGI-created cracks in the pavement that are very unconvincing. They do not appear to displace anything and - in a related continuity error - the cracks disappear in shots taken from ground level (the cracks are only visible in high-level 'looking down' shots.
Revealing mistake: When Mickey closes the wheelie bin lid, he then finds the plastic stuck to his hands, he lifts his hands up and the plastic stretches like tar. If you look closely when he lifts his hands up for the first time, you'll see that a shadow of one of his hands is cast on his shirt, but there is no shadow of the strands of plastic stuck to his fingers. Additionally, when he turns around to pull away from the bin, he crosses the strands over each other, but they are still parallel in the following scene.