The description of nuclear war. Granted, it was Sagan's informing people of this horror that helped to save the world from this fate, but...
The sequence in "Heaven and Hell" depicting the environmental destruction of the Earth set to Franz Liszt's "Totentanz".
"The Lives of the Stars" has an unsettling sequence depicting the death of the Sun from the point of view from the Earth.
The "alien abduction" sequence at the beginning of "Encyclopaedia Galactica" (pictured). Yes, it's debunked immediately afterwards, but only after scaring you quite badly! The music really doesn't help.
A Spacetime Odyssey
The camera pans over a selection of medieval torture devices after Neil informs us that Giordano Bruno was taken by the Inquisition. It is not good to imagine how those things were used.
The Hall of Extinction, which features sections devoted to the five previous extinction events, plus a blank corridor for whatever's going to wipe us out. (Fun fact, we built that corridor; if we end up on exhibit there, it's our own fault.) We also see a full demonstration of the Permian-Triassic Event, the worst of them all, which it's speculated the Earth took up to ten million years to recover from.
In "Hiding in the Light", the scene where Chinese scholars are being dragged to a giant pit to be buried alive.
Clair Patterson's visions of lead poisoning (pictured), manifesting as open wounds/infestations on everyone & everything around him, including a dog. Also counts as Nausea Fuel. A bit earlier, the Laughing Mad gas station employee running down the street.
Also from the lead episode: creepy advertising copy intended to market lead products to children. Values Dissonance and Science Marches On, right? Nope, Neil informs us earlier that the toxic effects of lead have been known since at least Ancient Rome (where the negative aspects of Saturn—who governed lead, among other things—lined up with the symptoms of lead poisoning).
Episode 11 starts the nightmare fuel with a depiction of really, really pissed-off gods that the ancients thought caused a decades-long drought, and it keeps going and going to all the things that can and have killed civilizations: asteroids and supervolcanoes, germs spreading across North and South America to kill 90% of the population, war and more war, and the things we're doing now in pollution and climate change which we could do more about and yet aren't.
The black hole. Even the Ship of Imagination is struggling!