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)
Continuity mistake: The cables on the window washer's bucket are fine until Foster shines her sonic pen on it. In the close up, the spot on the cables looks to be already cut and of course wired with the pyrotechnic device. (00:26:15)
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)
The Sontaran Stratagem (1) - S4-E4
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)
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.
Continuity mistake: In the scene where Cobb is briefing his troops, the troops all have their guns, but in the other scene (after you see the Hath marching) the troops are receiving guns. (00:15:45)
Other mistake: Just before the Doctor ignites the atmosphere, Sylvia's house is getting dangerously full of gas. When Sylvia and Wilf go outside after the air is cleared, the inside of their house is completely clear. Meanwhile, back at the Rattigan Academy, there is still gas lingering in the air. (00:34:43 - 00:37:15)
Factual error: The Doctor sets the atmosphere on fire, but only the upper part burns. The atmosphere extends from the Earth's surface (where it is densest) upwards, and so the flames would come right down to the ground, burning everyone to death. Of course that wouldn't work with the plot, so artistic licence has been applied.
The Unicorn and the Wasp - S4-E7
Factual error: In Lady Edison's flashback, she's reading "The Murder Of Roger Ackroyd", her favorite book. However, this episode is set in 1926, and the dust cover is from 2006.
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.
Continuity mistake: When Davros activates a screen in the Vault to show the Doctor and Rose the Reality Bomb test, the screen shows the prisoners being herded into the testing area, something that already happened shortly before. (00:23:14)
Factual error: Colonel Mace says the Sontaran ship is orbiting 5,000 miles (8,050 km) above the Earth. However, in shots of and from the ship in both this episode and "The Sontaran Stratagem", the Earth appears far too small for the ship to be that close, with the ship's true distance appearing to be well over double that. (00:08:34)
The End of Time: Part Two - S4-E18
Continuity mistake: When Wilf looks down while holding his service revolver at the end of his conversation with the Woman in White, the position of his right index finger changes between shots. (00:23:35)
Silence in the Library (1) - S4-E8
Continuity mistake: When the girl recognizes the Doctor on her TV, telling him that he was in her library, and he reacts, the position of her pencil crayon in her hand changes between shots. (00:20:45)
Continuity mistake: When Donna is sneaking around the Sontaran ship, she's carrying Martha's old phone, which she's using to stay in touch with the Doctor, and the rubber mallet from the TARDIS. There are times when one of the two objects, the phone more often, is missing from her hands with no explanation.
Continuity mistake: During Donna and the Doctor's conversation with an Ood at the reception who she approaches to ask if he's all right with being a servant, in shots facing the Ood, he's holding his translator ball higher than he is in wide shots and shots facing Donna. (00:11:50)
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.
Other mistake: When the Earth's nuclear launch sites are being brought online, country by country, in preparation for a strike at the Sontaran ship, Russia is puzzlingly omitted, even though North Korea of all nations is included. (00:17:20)
The Unicorn and the Wasp - S4-E7
Factual error: In real life, Agatha Christie's famous disappearance occurred in December 1926. This episode is quite plainly not set in winter, what with the outdoor garden party and lush green foliage.
Chosen answer: The Master knows that deep down, he deserves death for the crimes that he's committed throughout his life, and since he regards The Doctor as his arch-foe, he expects it to be at his hands. The fact that The Doctor is still willing to forgive him for all of his crimes hurts him more deeply than death would.
Captain Defenestrator