The Harry Alan Towers film adaptations are full of such moments. For example, in the 1965 movie, Lombard and the butler get into a random fistfight that lasts about one minute before the judge says "Now, now, that's enough"...and it is. It is promptly forgotten, and never brought up again.
Or the 1989 movie. There are several moments that fit this trope, but one that stands out in particular is the usual "Marston plays the full rhyme on the piano" scene that is usually in each adaptation (and ends up being crucial to introducing the rhyme to the audience)...except instead of actually playing the rhyme, Marston plays a few seconds of "Mad Dogs and Englishmen". Why? No one knows. And no one spends their time speculating on it, either.
Hilarious in Hindsight: A General MacArthur, written before World War II. As such, when the book was adapted into a play in 1943, MacArthur's name was changed to McKenzie.
It Was His Sled: All the guests are responsible for the deaths of someone while managing to escape the justice, Judge Wargrave is the killer and everyone is dead at the end of the novel. It's safe to say that someone who didn't already read the book should finish it before browsing its tropes. Of course, given that this is one of Christie's most famous books, this isn't surprising.
Misaimed Fandom: Let's just say that if the internet had existed when the book was first published, or if Agatha Christie had lived long enough to see the internet, she would have done a lot of head-desking at the discovery of how fans found some of her most intentionally despicable murderers to be sympathetic.
Christie was fond of having a sympathetic character turn out to be a murderer, because these types of characters tend not to be suspected by the reader. However, the notion that fans would still find these characters sympathetic after their guilt had become clear beyond a doubt would certainly make her mind boggle.
Mis-blamed: Rene Clair, director of the 1945 film version, received a lot of criticism for changing the ending of the book. A lot of people did not realize that the basic idea for the film's ending came from Christie herself, having changed it upon adapting the novel for the stage in 1943; Rene Clair simply brought about the Revised Ending in a different (and more convoluted) way.
Vera Claythorne's internal monologues in the book seem like this to some.
Anthony Marston's demise in the game.
A lot of the game can be incredibly narmy, mostly because of the cheap, limited animation and sometimes very poor voice acting.
Rogers' reaction to the death of his wife in the 1989 film. And his own death.
Blore's death in the 2015 miniseries. Instead of being bashed over the head by a marble clock shaped like a bear, Blore is stabbed to death with a carving knife while the killer apparently wears a polar bear rug like a poncho! Regardless of whether the killer could actually see out the open mouth, without the blurry-edged screen that implies that Blore thinks he's hallucinating it would look utterly ridiculous, instead of WTF?
Paranoia Fuel: in the 2015 adaptation, Lombard's flashback to his crime shows he wasn't alone when he did it; he was the leader of a four or five man team. Lombard even Lampshades this as to how the story got to U N Owen, saying 'it's amazing how people have an attack of conscience once they're home safe' (approx). What happened to the other men who participated?
Romantic Plot Tumor: Averted in the original novel, and to a certain degree in Agatha Christie's stage version and the 1945 movie as well, but the Harry Alan Towers adaptations put much more focus on the romantic subplot between the two survivors than on the actual mystery itself.
Philip Lombard justifies the abandonment of the natives with what amounts to "What Value is a Non-White?" (and Vera seems to agree— Emily Brent, of all people, calls her out on it!); he also refers to Isaac Morris as a "little Jewboy" and figures Morris called his bluff on his need for money because Jews just know these kinds of things.
The need to change the book's title (and the rhyme itself) over the years and the excision of terms like "nigger in the woodpile" also count.
More subtle, the main 'clue' of who the murderer is rests on the interpretation that he is the only character who is not guilty of the crime they are accused of committing. But from a modern perspective Judge Wargrave violated the criminal's right to due process under the law by getting the jury to convict him without evidence he was guilty beyond a reasonable doubt, so the reader may not reach that conclusion.
By contrast the 2015 BBC mini-series has a noticeable payload of f-bombs and similar- how much they would have been frowned on in real life in 1939 is hard to be exact for different social milieu, but it is definite that they would not have been allowed to appear in print before at least the 1960s.
the 2015 mini-series also has a couple of quick moments when Blore implies that Lombard is suspicious / the killer because he's Irish, and therefore must be a member of the IRA.
the reason that Vera committed a crime at all. All the portrayals of her are consistent in this matter: there's no implication that she wanted to marry a rich man, she just wanted to marry Hugo. Hugo was the one who refused to marry her without money; there's no indication that Vera cared about being 'provided for', or that she wouldn't have been happy to continue working if it meant they could be married. If their situation had happened in the 70's/80's onwards, Hugo would have simply have accepted their being a two-income couple and married Vera, meaning Cyril would still be alive.
Marston is killed first because the killer considers that the deaths he caused were accidental, so didn't deserve to go through the nerve-wracking tension the other characters do. Those deaths? He ran over two kids with his car, and with a Never My Fault attitude to boot.
However, it's also implied that he was killed first because the killer suspected that Marston was a sociopath and that his Lack of Empathy would have prevented him to be affected by guilt. He also thinks that Marston's attitude is caused by his upbringing, having not been taught the sense of responsibility as he was "amoral" and "pagan" (which, admittedly, is another kind of Values Dissonance). All in all, the killer's confession seems to imply that he killed Marston because he considered him a danger for the society, not because he wanted to make him suffer.
The confession clearly states that the murderer chose Marston from a number of similar cases because of his unique callousness making him "unfit to live".
Many, many fans find MacArthur to be the most sympathetic of all the guests. He was pretty much dead before he came to the island.
Armstrong committed a terrible accident that caused his patient's death, which not only haunted him and brought him to an island to be killed, he ends up becoming the killer's fearful pawn. Toby Stephens plays his woobie status Up to Eleven in the 2015 adaptation.
Likewise, Ethel Rogers was pretty much pressured into murdering her former employer by her domineering husband, and had to live with the guilt until she was ultimately murdered for the crime she didn't want to commit. This was why the killer chose to give her a relatively painless death.
Beatrice Taylor was fired by Emily Brent after getting pregnant and commited suicide after even her family had rejected her.
Whether by Vera or (in some adaptations) not, poor young Cyril was betrayed to his death by someone he loved and trusted.
WTH, Costuming Department?: The game has Vera dressed in a bright fuscia sleeveless dress which would have looked pretty scandalous in 1939, especially for a would be secretary/former governess. It doesn't help that her outfit is very bright compared to the subdued color schemes of the other characters, and a large portion of the game rooms.