Esoteric Happy Ending: Poirot tells the passengers he knows that they all had a hand in killing Casetti and how they did it, but ultimately goes along with Mr Bouc and Dr Constatine's agreement that the first theory — a stranger having jumped onto the train, killed Cassetti and left — is what they will give to the police. The entire Armstrong household has spent a long time figuring out this act of revenge and comes off scot-free for killing a man; even if said man deserves it. The novel depicts this as a pretty happy and nonchalant ending. Further adaptations actually went into the ethical question of whether this is or isn't a good idea.
Fräulein Schmidt comments on the murder of Daisy Armstrong, saying that a child's murder would be too barbaric an act for her native Germany. The book came out in 1934, and we all know what happened later on.
Possibly also an example of Getting Crap Past the Radar, Greta Ohlsson testifies to accidentally walking into the deceased's compartment in her nightgown and robe, receiving a comment of "You're too old" in response. Now remember why he was killed.
Mrs. Hubbard's constant chatter about her daughter and grandchildren when it's revealed one of her daughters and both of her grandchildren are dead.
It Was His Sled: Everybody knows what happened, even without reading the book.
Strawman Has a Point: On both sides. Poirot, in the David Suchet version, is correct in that people should always try to choose law and order over vigilantism; the social contract of the law is often the only thing keeping a civilization from falling to anarchy. However, the passengers retort that they already relied on lawful means to punish Cassetti, which only resulted in failure and further grief for them.
Tear Jerker: The murder of the baby Daisy Armstrong and tragic fallout resulting in several more deaths.
A mild example, in Poirot's referring in his notes to one of the passengers as an "American subject". Americans find it politically objectionable to be called subjects (to whom?) rather than citizens.
Poirot noted, when he was contemplating all of the passengers in the coach and their numerous nationalities, that "only in America" could such a gathering occur. This is used to help him deduce they were all part of the Armstrong household or had connections to the family, and start "casting" them in roles... but not only are some of those role-castings themselves based on outdated views of the nationalities in question, but it becomes rather Harsher in Hindsight considering a) the melting pot view of America has become rather dismissed and fallen out of favor in the years since then and b) thanks to views on immigration changing, it's far less likely such nationalities, or a household containing them, would be as accepted or celebrated today. Even in the time the novel was written, Americans were not nearly as accepting as Christie depicts them (issues with immigrants being a Cyclical Trope, things weren't as bad as in the 1800s, but the stigma was still there), making this another aspect of her Eagleland views. For that matter, many European nations are becoming heterogenous enough that such a mix wouldn't be any less likely there than in the U.S.