Script versus short story
Beacham stays largely true to the source material, with certain important additions. The adaptation opens with a visit by Rupert Carrington to Florence in her flat, and the arrival of the Count at the 'Adelphi' (the Ritz in the story). Moreover, there's a subplot involving stocks in a mining company (Yellow Creek), which interests Hastings, of course. In the adaptation, Halliday (who is Australian and called Gordon here) consults Poirot before the crime takes place. At first, he wants him to look into the issue of the Count, and Poirot and Hastings observe the couple at the Adelphi. Later, when Florence disappears on her journey with the Plymouth Express, Halliday again consults Poirot to ask him to find her. Of course, she is found murdered, and that's just about where the original story comes into the picture. There are important additions to that section too. For instance, Poirot and Hastings travel down on the train to interview the paper boy (mentioned in the story), and he remembers Florence/the culprit because she asked for the late edition of the paper, not because of a large tip. This later turns out to be a plot point, as the Count had to know whether his stock speculation in Yellow Creek had succeeded. Moreover, Miss Lemon is added to the plot, and she finds the early and late editions of all the major newspapers. Hastings gets to "interview" Rupert Carrington, whom he tracks down in a bar. Carrington is trying to escape his creditors. Also, the jewel thief (McKenzie here, Red Narky in the short story) is discovered in Miss Lemon's archive, not by Japp in the Scotland Yard files (a bit unbelievable perhaps, but a nice way to include her filing system). All in all, though, it's a nicely done adaptation with only minor changes. Even if I wish they had skipped this one, knowing that they would later get to The Mystery of the Blue Train, a very similar story. Perhaps they could have done 'The Lemesurier Inheritance' as a 50-minute episode instead? Oh, well.
Directing, production design, locations, soundtrack
Piddington makes great use of the train location, there are several nice shots of the station and the train in motion (some of which I think we'll see again in a few later episodes). The production design is faultless as always. Of locations to note, there's Du Cane Court, Balham and The Adelphi Building on the Strand, London. The soundtrack is very nice, once again by Christopher Gunning. He released it on the first Poirot album, but it was removed for the re-release. Luckily, it's available on YouTube at the moment.
Actors and characters
It's nice to see the series (and Poirot) gradually explore darker territory. I admit I might be reading things into his performance, but Suchet's reaction as Halliday points out Poirot isn't a father so he can't possibly understand what it's like to worry seems to me to hint at the emotional sides of Poirot. Also, the crime itself is displayed in the most graphic way of any of the episodes, I think, both in the flashbacks and in Poirot's retelling of it. Of the guest actors, there are no real standouts. Julian Wadham (Rupert Carrington) is of course a face many will recognise these days, he seems to pop up in nearly every British television series. Alfredo Michelson is over-acting as the Count. I guess it's a difficult role to play convincingly, but still.