Aborted Arc: At the end of The Cosmic Computer, the main characters on the planet Poictesme are setting up plans to eventually help rebuild civilization after The Federation falls, with the aid of the advanced computer Merlin. They won't themselves live to see the collapse, much less the rebuilding, but they're preserving, as best they can, the capability to rebuild. None of Piper's works set after this make any mention of Merlin or Poictesme; for whatever reason, the Merlin Plan failed without a trace.
Funny Aneurysm Moment: Five years before JFK was assassinated, Piper wrote Lone Star Planet, in which the politicians of New Texas were routinely offed if they "had it coming".
This was based on a notion proposed by H. L. Mencken, and it wasn't quite that routine; a court looked into each killing (or thrashing), with the assailant having to provide proof of what the politician did that deserved what happened to him. In the trial on which the story focuses, practically no one on New Texas feels the murder of Silas Cumshaw was justified. Plenty of people, instead, feel it'd be a good thing to wipe out his killers, and anyone who helped his killers....