What did the astronauts fail to do which would have saved them from falling haphazardly through space?

They failed to prevent the rocket from exploding by failure to press the SCE (Signal Conditioning Equipment) switch.

Explanation:

In November 1969, Apollo 12 commander Pete Conrad with his crew members were on their way to the moon. This happened four months after men first set foot on the Moon. Due to the euphoria in the success of Apollo 11, NASA decided that Apollo 12's mission should be more aspiring.

Pete Conrad was aiming for a precision touchdown but the rocket was hit by two lightning strikes which made him lose control of the rocket for a while and the space craft began falling till haphazardly till a crew member suggested the SCE switch should be pressed.

SCE stands for Signal Conditioning Equipment, the system that processed spacecraft sensor data for transmission to the ground. It was pressed after which they managed to steady it and later successfully landed on the moon.

"Kaleidoscope" is the second story in Ray Bradbury's science fiction anthology The Illustrated Man. The story narrates the fate of a group of men who narrowly escape an explosion on their rocket ship but end up abandoned, floating away from each other in space. In the opening lines of the story, the men are described as "wriggling silverfish" who are "scattered into a dark sea," which emphasizes the desperate, hopeless situation they face.