Revealing mistake: When the Doctor and Donna are attempting to smash open a window while stuck in the window-washing cart, there is a shot of them from above just before Foster cuts the cable in which banging sounds are heard and the cart is shaking, but if you look closely at them they aren't actually touching the window at all. (00:26:10)
Continuity mistake: The house that Donna and her family are shown living in in Series 4 is different from the house the Doctor dropped her off at at the end of her first appearance, "The Runaway Bride." You would assume they'd merely moved - except that in this episode, Donna and her family are shown living in their Series 4 house before the events of "The Runaway Bride", on the day Donna gets the job that leads to her meeting the Doctor in the first place.
Audio problem: During the climax, when the Doctor has Wilf's old service revolver and is alternately pointing it at the Master and Rassilon, there's a cocking sound every time he turns. Not only is the handgun a revolver, so it only needs to be cocked once, the Doctor is only shown actually cocking the gun once, when he first points it at Rassilon. (00:44:10 - 00:45:55)
Other mistake: Shortly after everyone arrives on the Vinvocci ship, when the Vinvocci and the Doctor run through the door on their way to the flight deck, the Doctor comes back to get Wilf, who didn't initially follow because he was mesmerized by the sight of the Earth from orbit. It's obvious that David Tennant went just behind the door and paused briefly before coming back into the room, which is not what the Doctor is supposed to be doing. (00:16:00)
Visible crew/equipment: While the Doctor tries to get into the data core (after Proper Dave tried) it cuts to the telephone still ringing, and when the young girl asks her dad why he's not answering the phone, just as he tells her that the phone is not ringing the boom mic dips into view at the top of the screen. (00:19:40)Super Grover
Revealing mistake: In the beginning, the ATMOS system takes the car to the Thames, then runs it into the river. At first, the car runs forward normally. After the angle change, there's a huge white cloud of mist behind the car that dissipates quickly, meaning an air cannon of a sort was used to propel the car into the river. (00:02:35)Movie Nut
Other mistake: Near the start, the Doctor and companion, just after having experienced a violent earthquake within the city of ancient Pompeii, discover someone sold the TARDIS after fleeing toward where they parked it and finding it gone. But where it had stood there is a floor to ceiling shelf of clay pots, very aligned, unshaken, unmoved from the shelves. (00:04:00)James G. Mason
Continuity mistake: In the TARDIS as Donna navigates, the Doctor uses a hammer to help correct the trajectory, then rests it on his neck and shoulder. A second later, when the phone rings, his hand, holding the hammer, is suddenly much lower, below his waist level. (00:03:15)Movie Nut