With "The Assignation," Poe reverts back to the mode I've personally found so dissatisfying: the ironic know-it-all who tells some story that has neither sound nor fury, and still signifies nothing.
The tale's told by an unnamed bystander who witnesses a weird melodramatic incident in the canals of Venice. Somehow or other, an infant child is precipitated into one of the watercourses. The child's mother, known as "the Marchesa," watches in consternation as the servants of her husband, a powerful man named Mentoni, try and fail to locate the child before it freezes in the icy water. Somehow the servants can't seem to find the kid, and Mentoni, watching silently from a window, doesn't seem too concerned about the baby's fate. The narrator then sees a dashing young man dive into the water, unerringly dive into the water, and bring the living, though very damp, child back to its mother. The incident seems to mean nothing, though the narrator befriends the young man, known as only "the stranger." The two men go back the latter's apartment, which is full of rare, precious art. Then the young fellow makes some wild pronouncements, drinks a glass of wine, and dies of poisoning-- just as a page serving the house runs in and announces that the Marchesa has also died of poison.
I got absolutely nothing out of this story but Poe's tedious need to show off his erudition, and though I presumed by the title alone that some indiscretion had been committed, the story gave me nothing to go on. The Internet rescued me with this essay, arguing that Poe was satirizing an allegedly biographical story by Thomas Moore. This sounds like the best possible solution, but knowing this doesn't make the story read any better.
In the comments-section of this online essay, a poster named Amper offers an even more intriguing reading: that the narrator is a hired gun, responsible for executing two clandestine lovers on the orders of the jealous Mentoni. If this could be conclusively demonstrated, then "The Assignation" would stand as a direct predecessor to the much more effective "Cask of Amontillado." But I still consider "Assignation" an artistically sterile exercise.