These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: 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.
Fridge Brilliance: Even if there'd been a last survivor, the killer might still have gotten their way. Whomever was left behind on the island would naturally be blamed for the murders, and hanged for them. (Technically that wouldn't match the poem's suicide, but it could be Metaphorically True that they'd put themselves into the noose by committing their original crime, and then coming to the island in the first place!)
Vera finding three unbroken figurines makes sense when you consider that the killer was accounting for Blore's death (as Vera and Lombard had definitely seen his body), but not Armstrong's (as he didn't know whether or not they had discovered his body yet).
Fridge Horror: What exactly did Fred Narracott do to deserve being the man who found the 10 dead bodies?
Fridge Logic: In addition to the three clues acknowledged by the killer, there are additional reasons not mentioned that would lead an investigator to the killer. The investigators consider that U.N. Owen must be one of the ten dead people. The murderer, who is terminally ill should come under suspicion as one willing to commit suicide.
Although the book mentions that the purchaser of Indian Island covered up the financial tracks, an investigation of the victim's accounts should reveal suddenly missing money invested in dummy corporations.
And indeed the murderer would have to be someone wealthy enough to buy an island. That rules out nearly all of them.
Judge Wargrave sending himself a letter of invitation to the island is a pretty slick move, since it could be used as cover later if the group members try to establish their legitimacy by showing that they too were invited by the murderer. However, in his first scene, Wargrave clearly reads the letter to himself as if he's never seen it before, recalls the woman who supposedly sent it to him, and takes a few minutes to wonder about the identity of the island's mysterious owner. None of these things make sense if Wargrave orchestrated the murder plot.
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.
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.
And then there's Philip Lombard, who is something of an Anti-Hero in the book regardless of what he did. The Russian film version, however, changes that. He ceases to be even a semi-likeable character when he rapes an already mentally unstable Vera Claythorne, and it is subtly implied this plays a part in her breakdown at the end.
Lombard's event horizon is subverted in the original black & white movie, in which it is revealed that he is not Lombard but a friend of his impersonating him after the real Lombard recently committed suicide.
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.
Nightmare Fuel: There's a reason Agatha Christie is known as the grandmother of the slasher film and that reason is And Then There Were None/Ten Little Indians/Ten Little Niggers. A particularly nightmarish moment involves the incredibly effective use of seaweed!
"Don't you see? We're the zoo!" Shiver.
Emily Brent's hallucination of the dead Beatrice Taylor walking towards her fits here too. Especially if you know what she has done to the girl.
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.
They Just Didn't Care: All three Harry Alan Towers films changed the locale of the story, as well as most of the character names, for no identifiable reason.
Some of the character names were changed to accommodate the nationality of the actor playing the role; for instance, Anthony Marston became Prince Nikita Starloff when Russian-born Mischa Auer was cast in the 1945 version. However, for many of the roles, no discernible reason for the change exists. (Why was Vera Claythorne's name changed to Ann Clyde in the 1965 version?) Lombard's first name was changed to Hugh in the 1965 version as a nod to actor Hugh O'Brian, but it inexplicably remained Hugh in the 1975 version, which featured Oliver Reed in the role. William Blore is the only name to remain consistent through all the adaptations.
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.
The Woobie: 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.