The story is a prequel to the events in The Hitchhiker's Guide to the Galaxy and has the young Zaphod Beeblebrox working as a salvage ship operator. He guides some bureaucrats to a crashed spaceship that may be leaking some dangerous materials, radioactive, toxic and otherwise hazardous by-products which were destined to be thrown into a black hole. The bureaucrats swear that it is "perfectly safe". When asked why they want to see it if that is true, they claim "We like looking at things that are perfectly safe". The comic asides in the story include some of the time travel paradoxes which are a common running theme in Adams' SF work, and plenty of material about lobsters.
Throughout the story, it is emphasized that there is something particularly dangerous on board that ought to have been utterly destroyed, but is feared to have escaped.
Ultimately, it is revealed that the something was actually three identical "Designer People". The personalities seem totally benign, which is what makes them so dangerous. The ship is filled with substances so dangerous that they are safe because no one who would actually use them would be let near. The personalities, products of a Sirius Cybernetics Corporation project, however, have custom personalities that could not naturally exist. There is "nothing they will not do if allowed, and there is nothing they will not be allowed to do." Since no one will recognize that they are capable of mass destruction (despite their good intentions), no one will stop them from doing the unspeakable.
The story culminates with the revelation that one of the personalities has escaped and headed off into Galactic Sector ZZ9 Plural Z Alpha, which is where Arthur and Ford Prefect were picked up by the Heart of Gold a fraction of second before they perished (and just minutes after they had been rescued from the demolished Earth in the same sector), in the original Hitchhiker's Guide to the Galaxy.
Though it does not state it specifically, the story implies that this unspeakably dangerous creation is now known to the planet Earth as then-President Ronald Reagan, a reflection of the author's antagonistic attitude toward the President which also surfaces in Mostly Harmless. A version of the story included in the posthumously-published The Salmon of Doubt makes this explicit.
Another implication of the story comes in its final sentences. One of the officials says that Galactic Sector ZZ9 Plural Z Alpha must be made "perfectly safe". This would provide an explanation for the Vogons' task of destroying Earth in Mostly Harmless.
A man invents an aorist rod to mine energy from the past, and within a year tracts of the past were being fully drained. Those who complained were accused of an "extremely expensive form of sentimentality", as the past was a cheap, clean and plentiful source of energy. Anyone who said "draining the past impoverished the present" was told to "keep a sense of proportion".
Only when the people realised that the "selfish plundering wastrel bastards up in the future" were doing the same thing to their era were aorist rods banned. "They claimed it was for the sake of their grandparents and grandchildren, but it was of course for the sake of their grandparent's grandchildren, and their grandchildren's grandparents."
In 2007, a group of fans on the Douglas Adams Continuum adapted and produced a non-profit fan-based radio episode of Young Zaphod Plays it Safe. The episode lasts around 22 minutes and can be found at the link below.