Appointment with Death is one of my favourite Christies. It perfectly represents what the best of her craft is: a clockwork plot, subtle clues, simple but effective character sketches, and a logical solution which still surprises. It's a Golden Age detective story down to the last detail, including the atmospheric title.
While in Jerusalem Poirot overhears this chilling exchange between brother and sister: "You do see, don't you, that she's got to be killed?" Later, when an evil old matriarch dies, Poirot investigates her stepchildren, a bunch of repressed basket cases who lived under her thumb.
The stepchildren are like caged animals freed by her death. Christie was a staunch conservative who supported the death penalty and believed that the world would be better off without some people, a belief reflected in how her characters here develop after the murder.
As usual there's romantic subplots, which are neatly resolved in the epilogue. They work here because Christie doesn't let them distract us from the puzzle, like she sometimes does (as in the tortuous Murder is Easy). Suspense and atmosphere languidly uncoil like a snake. The announcement of the murder is a beautifully written scene.
The novel's latter half is mostly dialogue, with some chapters containing almost no other prose. This style might daunt some readers, but they're unlikely to be reading Christie anyway. The denouncement is splendid in its grand procession of logic.
Appointment with Death is the embodiment of classic mystery fiction. An excellent read for fans of this genre.