The Impossible Planet (1) - S2-E11
Factual error: The Doctor (and the staff on the station) refer to the idea of a planet being in orbit around a black hole as 'impossible'. It is not. Gravity (and physics in general) works perfectly well outside of the event horizon. For all practical purposes - regarding orbiting around it - the black hole might as well be any other object, as long as it has an equal mass. (00:07:15 - 00:08:30)
The Impossible Planet (1) - S2-E11
Factual error: Ida, the science officer, says that the planet is in geostationary orbit around the black hole. However, the word "geostationary" applies very specifically to objects orbiting the planet Earth. Since a black hole is a type of star, this planet's orbit could be described as astrostationary, or even just stationary, but definitely not as geostationary. A science expert on an interstellar mission wouldn't make this mistake, and she wasn't dumbing things down, either, since "geostationary orbit" is already a pretty obscure topic for people unfamiliar with space technology. (00:07:40)
The Impossible Planet (1) - S2-E11
Factual error: The graphics depicting the black hole show matter falling directly towards the centre of it. This would only happen if all the matter happened to be heading in that direction already. In reality, matter approaching the black hole at any other angle would swirl around the event horizon, like water going down a plughole.
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