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)
Revealing mistake: When the Doctor and Donna are walking through the underground tunnels towards Mount Vesuvius, tunnels that can be presumed to be fairly warm due to their connections to volcanic activity, their breath is visible - something that only happens in cold temperatures. (00:31:20)
Revealing mistake: Soon after the Doctor and Donna are blasted back there is fake snow on the camera, indicating there's a camera there. (00:34:15)
The Sontaran Stratagem (1) - S4-E4
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)
Silence in the Library (1) - S4-E8
Revealing mistake: When the Doctor notices the unnatural triangular shadow signalling the presence of the Vashta Nerada and points it out to Donna, the shadow appears over Donna when she's standing in front of it, showing that it's a special effect added to the shot afterwards. (00:11:10)
Silence in the Library (1) - S4-E8
Revealing mistake: Also applying to the second episode of the two-parter, "Forest of the Dead": The keyboards on the Library's computer terminals are very obviously standard Apple keyboards - this in an episode set in the 52nd century.
Revealing mistake: In the opening scene the Doctor and Donna are speaking over the phone. The purple phone Donna is holding shows the slot where a cable should be plugged in, but there is none. (00:00:25)
Suggested correction: This shouldn't be considered a mistake. While it's true in real life this phone has a slot for a cable, they're on an alien planet and this is unknown technology. In-universe there's no way of knowing what that slot is for, and there's no reason to think the phone needs to be plugged into anything.
Revealing mistake: When the Doctor and Donna run back inside the TARDIS to find the console room lit up in red and the Cloister Bell ringing, what's visible outside of the doors as they run in isn't the bright Shan Shen street the TARDIS is parked on but the dark soundstage the set was built in. (00:47:49)
Revealing mistake: When Torchwood is transmitting a signal to the Doctor, there is an overhead shot of Cardiff in which several shoppers are idly walking through apparently deserted streets. (00:31:55)
Revealing mistake: The Cyber-Leader has a clear section in the top of its head through which its brain can be seen. The brain in question is very obviously plastic.
Revealing mistake: Adams, the female Vinvocci, has a tendency to wrinkle her forehead, which makes the fact that her spiky head is a cap the actress is wearing very obvious.
The End of Time: Part Two - S4-E18
Revealing mistake: When Addams is telling Rossiter not to respond the Master's message, a patch of non-green skin can be seen on her face showing where the makeup wasn't fully painted on. (00:27:50)
The End of Time: Part Two - S4-E18
Revealing mistake: When the Doctor is being rolled down the stairs whilst he is strapped to the chair, it is apparent that in the wide shots, it is a dummy in the chair and not the Doctor. In the wide shots, the Doctor is sitting virtually still and motionless, but in the closer shots, he is fidgiting.