In murders, nothing should be taken for granted. Especially Agatha Christie's. In several of her novels, she had the investigators looking into a murder that did not exist, a person that did not exist, a motive that did not exist and many other red herrings.
Hence, when the good Rev Stephen Babbington died during a party thrown by retired actor Sir Charles Cartwright, none of the guests present appeared to be who they were supposed to be. There was no motive, nothing was left to show the death was a criminal act.
Some time later, Dr Strange who was also a guest at the party died, this time, the nicotine poisoning was clear.
Told primarily from the perspective of Sir Charles Cartwright, his friend Mr Satterwaithte, and modern girl "Egg" Hermione Lytton Gore, Hercule Poirot took the passive role most of the story. The other three went about gathering clues, examining scenes of the crime and interviewing the usual suspects.
The only problem with such an approach could be revealed by one of Christie's favourite dogma : people do not tell what they saw or heard, they tell what they thought they saw or heard.
In many instances, it was merely written Sir Charles, Mr Satterwaithe and Egg reported what had happened to Poirot rather than describing the words they used to convey the information to Poirot. Therein lies one of the weakness of this book.
A second weakness of the book was some of the offstage investigation work done by Poirot was not revealed to the readers. In stories where the clues for opportunities and accessories were (subtly) evident, motive was not as vital for the readers to correctly guess the solution. However, this story was weak in all but the opportunities department. Only the camouflaged opportunities was masterfully done by Christie for both deaths, requiring people to consider things in the opposite of the conventional direction.