Agatha Christie was actually exploring real thematic material in this seemingly simple who-dun-it mystery with Hercule Poirot. Inspired by the American kidnapping and death of Charles Lindbergh’s two-year-old son, Christie explores the American justice system and the international Western accord on the concept of justice. A criminal in America, Ratchett (Cassetti), whose crime was against a child (like the Lindbergh case), escaped conviction and punishment because he had an influential "secret hold ... over various persons." He is pursued by those who are outraged by the violation of legal justice and who decide to take justice into their own hands. A vigilante jury of twelve is formed. A ruling for conviction is passed, and an execution is arranged.
Since Christie used the Lindbergh case as the inspiration for the story, the largest theme is the pursuit of justice. She asks about the validity of legal justice that can be swayed by influence and money. She asks about the nature of justice and its association with a quorum of twelve honest people. She asks how far honest people may rightly go in the pursuit of justice if legal justice has been corrupted.
While there are are also strong thematic questions raised about law and justice in America specifically, since the Lindbergh case occurred in America and her characters were victimized in America in "the Armstrong case," the international cast of characters from different socioeconomic ranks raises the question of justice to a higher, more universal consideration.
"How many wounds are there exactly?"
"I make it twelve. One or two are so light as to be practically scratches. On the other hand, at least three would be capable of causing death."
"The question we have now to ask ourselves is this," [Poirot] said. "Is this murder the work of some rival gang whom Cassetti had double-crossed in the past, or is it an act of private vengeance?"