This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / Spitting Image
Spitting Image: Because you can't spell "satire" without "AIEEEE!!"
The grotesque faces of many of these puppets! To make matters worse, as the seasons progressed the puppeteers were able to make them appear more life like, with eyes blinking and sometimes letting real humans stick a puppet head on their own body, making it all cross dangerously into the Uncanny Valley territory.
The final sketch of the first season, where the sun sets and various puppets of politicians and dictators pass by, set to a special version of The Police's "Every Breath You Take", sung by Sting himself! What makes this scene so disturbing is that the sun sets as if a nuclear war has taken place and everything on Earth is dead. Made especially chilling by the face of the Grim Reaper appearing in close-up near the end of the song.
There was a sketch where Ronald Reagan is in the White House and hears that Thatcher told him: "You can launch those missiles over my dead body." Reagan, Completely Missing the Point, says: "Ah, good ol' Maggie. I can always count on her.", whereupon he pushes the button for world destruction with the words "Goodbye, world!"
In the first season Norman Tebbitt's puppet puts Robin Day's hand in a blender!
Most disturbing aspect: after a while certain real life celebrities eerily started to sound and look like their puppet caricatures.
In some ways,the Chernobyl episode. Though there is a scene missing in this specific compilation. In the original broadcast where the Four Horsemen of the Apocalypse talk about how they wish this "was all over", Ronald Reagan comes out of the darkness and laughs: "Not long now, guys." This implies that he will soon nuke the rest of the world into smithereens. For some reason the uploader didn't include this part. Here's the full episode...
This image of Reagan and a truly frightening looking ayatollah Khomeini: