The cook had prepared two plum puddings, a large one for Christmas and a smaller one for New Years. The larger one was dropped while being cooked and it was stated that the smaller one was served at Christmas but during the meal it was obviously the larger pudding served.
Poirot appears to arrive at the Colonel's house with less luggage than when he departs.
The characters are seen stirring Christmas puddings on Christmas eve. Traditionally, Christmas puddings are made around 5 weeks before Christmas, which allows their flavour to develop and intensify. This day is known as Stir-up Sunday - when everybody takes a turn to stir the pudding for luck.
While it is possible that the family in this episode completely abandoned these traditions, it would be highly unlikely in the social context and era.
Prince Farouk of Egypt is said to be 19 years old. In reality, Farouk was only 16 when he succeeded his father Fuad I as King of Egypt on April 28, 1936.
The shot of Annie the maid during the family's introduction to Poirot is a stolen shot from the final scene where Poirot tells her she has his eternal gratitude.
The supposedly ancient Egyptian ruby is shown as a faceted stone. Faceting of gemstones only started in the late 13th and early 14th centuries. Prior to that time, gemstones were works into cabochons; which is to say they were simply shaped and polished, but were not faceted.
Poirot asks Desmond Lee-Wortley (Nigel Le Vaillant) to check the pulse of the, apparently, murdered girl. This was a ruse set up by Poirot and the girl was only pretending to be dead. Lee-Wortley feels the wrist where a pulse would be felt, but he says "No, nothing". He would have felt the pulse and realised that it was a trap set by Poirot.