Factual error: Attention to detail in props is always extremely high in this series, and tubular flashlights have been in circulation since the beginning of the century. However the one that the supposed burglar is holding as they make their way through the top floor of the villa looks perfectly modern and unlike any model compatible with the 30s. (00:10:20)
Factual error: Hastings and Miss Lemon decide to investigate on their own. In the outside view of the first suspect they go question, a large contrail is visible on the left of his building (contrails were not a complete impossibility in the 30s, but it's rather odd to randomly see one in an establishing shot for this timeframe). (00:22:40)
Factual error: Poirot is visiting an art exhibition with the Countess, and expresses his admiration for a painting by Marc Chagall. Amazingly enough, that painting is "Les Plumes en Fleurs", something Chagall will create in 1943, years after the time when this pre-WW2 episode takes place. (00:24:50)
Factual error: At the party, Marcus Hardman tells Bernard that the Countess recently arrived from Russia, and she describes herself as being in exile. Which made sense in the source material, set right after the Russian Revolution, but less sense in this adaptation, set in the mid 1930s. If she stayed in Russia that long, she would have spent 15-20 years with zero privileges from her rank at that point, and nothing from her old wealth, seized by the communist government.