Cargo Ship: The narrator has an extremely sensual relationship with a woman's bicycle Sergeant Pluck keeps locked up in the cell. This was completely intentional on the part of O'Brien. It also serves as a Brick Joke for Sergeant Pluck's concerns about bicycles becoming sentient.
Eldritch Abomination: O'Brien himself seems to have come to regard the book as this. One critic has argued, based on the book itself and the author's correspondence, that he wrote it thinking it was basically a comic novel, and when it kept getting turned down he re-read it, found it frightening and decided not to publish it, instead telling everyone that he'd lost the manuscript.
Ho Yay: between the main character and John Divney.
Vindicated by History: O'Brien was unable to find a publisher for the book in his lifetime. He reused some elements of the book for his last novel The Dalkey Archive, but gave up trying to publish The Third Policeman — in fact, he was so ashamed of his failure that he claimed to have lost the manuscript whenever anyone asked him about it. It was only after his death that it was rediscovered (he had kept it on a table in his lounge the whole time), published and quickly hailed as a masterpiece. The Dalkey Archive, by contrast, is regarded as not nearly as good.