So, in this episode we become much more precise about exactly when these episodes are taking place. The episode begins with the bonfires and firecrackers of Guy Fawkes night, which Anglophiles will know takes place on November 5th. Halfway through the episode, Poirot dictates a letter which references a previous letter supposedly written in March of 1935, so it's safe to assume that the episode takes place in November of that year, or 1936 at the latest.
As Poirot and his companions observe the fireworks that night, Hastings suggests that the general noise and chaos would make it a good night to shoot someone. The next morning they find that the idea has evidently occurred to someone else, as a woman's body is found in her home. She appears to have committed suicide, but there are indications that it may have been murder instead. Poirot and Japp sift through ashtrays, garbage cans and cupboards to find the truth.
On the one hand, I was fascinated with the production values: the costumes,the nightclub, the Art Deco design of the house where the crime took place, and especially Poirot's apartment, with its semicircular minimalist bookcases and gleaming surfaces. I could have paused every few minutes just to appreciate the trouble they went to to recreate the look of the era.
On the other hand, one of the period aspects they recreated was the colonialist view of the English at the time (which is sprinkled throughout Christie's novels and short stories). It's only natural that her work should reflect the prevailing attitudes from almost a century ago, but it is jarring to hear Poirot and Miss Lemon discuss the difficulty they are having communicating with the local Chinese laundry. (Here I am forced to admit that I laughed out loud to hear where Miss Lemon got the pidgin English phrase she used with the delivery boy. Vaguely racist, but still funny.) Another minor point related to the reflection of the times. One of the characters, described as an unsavory type, is said by a witness to have a toothbrush mustache. I believe this description came directly from Christie's short story. But when we see the character only a day or two later, he has a significantly longer mustache. I suspect that in 1935 that style was relatively popular, but Hitler's use of it had made it so unacceptable that people were unwilling to show it even in 1989 when the show was filmed. This is what comes of trying to depict bygone times with authenticity.