"Dead Man's Mirror" is too complex a plot to cover well in a 50-minute film. This great mystery needed a full-length movie to do more justice to the number of interesting characters. Still, it's a tremendous story in the Agatha Christie tradition. Both Captain Hastings and Chief Inspector Japp accompany Poirot on his sleuthing - although no one else really has a clue (including we of the audience) until right at the end.
This is another mystery that has some of the occult in the plot. It strikes one as funny that in such films, the background music takes on a distinctive eerie sound. I suppose it's the Hollywood effect of trying to build buy-in to the occult notion. All that would be to raise speculation as to what mysterious forces might be at work. For most viewers though, such nonsense immediately smells of a red herring. That's okay - it's all part of the fun.
At one point, Poirot says, "Poirot interests himself always in matters of the occult." One wonders how many people thus might think that Poirot or Agatha Christie (or both) believe in the superstitions of the occult. Rather, Poirot knows of the power that belief in sorcery and such can hold over a person's sanity and senses. Again, for the movies it's all fun and adds to the story, if only with distraction.
Here is a favorite exchange of dialog from this film.
Captain Hastings, "Oh, I take it you'll refuse?" Hercule Poirot, "To refuse, yes, it is my first instinct. But you know, Hastings, a man with so much arrogance as this - even he may be vulnerable in ways he cannot see." Hastings, "And, he did offer you that mirror." Poirot, "That too." Hastings, "I'll get the tickets tomorrow."