At one point two characters are described leaving the Royal Opera at Covent Garden at the interval between Act II and Act III of the opera that night, which is revealed earlier in the story to be Mozart's Don Giovanni. One of the most famous and popular operas ever written, Don Giovanni has only two acts.
At 19:57, Inspector Japp brings two bottles of Guinness (Irish stout beer), mentioning "James's Gate Dublin" on the label, instead of "St James's Gate Dublin"
As the butler falls through the skylight the zippered bag magically pops open allowing money to fly all over the place. In addition his body is seen lying on top of a large number of bills which is also impossible since the bills would flutter to the ground landing well after the body so they could not possibly be under it.
In the pre-television era, it's hard to believe that the voice and mannerisms of Poirot were well enough known to the public that he would be the subject of a cabaret impersonator.
When the butler runs up onto the roof just before he falls you can clearly see a Cessna 172 in the background, a plane not invented or made until many years later in 1955. Also during the chase a modern TV aerial appears in the sequence.
Miss Lemon places a Picquotware kettle on the stove to boil water for tea. This kettle was designed in 1938, but did not go into production until after the war, so it would not have been available in 1936, when the story takes place.
When Lucie Adams arrives to visit her sister Carlotta (who has already been murdered) her taxi pulls up on modern double yellow no parking lines.
When the butler falls through the airport roof you can see the inflatable crash mat when the butler lands on it.
During her revue, Carlotta Adams refers to Adolf Hitler as "Germany's new Chancellor". However, her letter to her younger sister (Lucie) reveals that this is June 1936, when Hitler had been in power for over three years.