While also listed as a Crowning Moment of Funny, the scene where the engineer is trying to explain the mecha problems. All these full-grown adults are coming up with ideas for a giant robot designed to kill thousands of people at the very least like little boys playing a game.
The events that transpired in the science room also qualify, both in story and out.
The entirety of Koizumi's stay at "Friend Land" tapped directly into a person's small, natural measure of paranoia very effectively. The "Bonus Level" arc was especially creepy.
The few moments where Urasawa drew mysterious characters in a stylized ghostly art-style. Specifically Professor Shikishima's daughter in 21st Century Boys when she was shown in her creepy nurse outfit with those cold dead eyes.
Koizumi being forced to stay at Sadakiyo's house while he puts on his best Norman Bates impression.
The reveal that there were three boys wearing masks.
The lab incident. Fukubei in hanging from the ceiling with a rope around his neck, ecstatic beacuse he made the others witness a miracle... and then begins to choke. No wonder poor Donkey jumped out of the window.
Majoume has a disturbing encounter with Friend in the virtual reality game, and exits to see Friend, disconnected from the game, standing over him. Not only is this freaky as hell, it's a major hint that there is more than one Friend.
The end of the virtual reality game, when Friend takes off his mask and you see old Sadakiyo's head attached to a kid's body. And just everything about Tomodachi Land, really.
Fukubei looks in the mirror. He has no face.
That freaking tower with the eye symbol. There's something utterly disturbing about that.