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.
Award Snub: Some may see Tommy Lee Jones losing out the Oscar to Jack Palance as this, or at least when one sees how it might have led to his win for The Fugitive over Ralph Fiennes in 1993.
Possession Sue: In real life, Jim Garrison was a deeply eccentric, volatile individual, popular to some degree but mistrusted by a great deal of New Orleans. He had a raft of incredibly bizarre theories about people he tied to the assassination case (his actual logic for the "Clay Bertrand" alias was that "[homosexuals] change their last names, but not their first names"), and was willing to subject witnesses to hypnosis and "truth serum" in order to get the story he wanted. The Clay Shaw trial was a sham, in which Garrison did everything short of set fire to the Fifth Amendment, and the judge was vocal in his disgust at Garrison's behavior; the jurors only took a half-hour to find Shaw innocent and reported in their statements that they were appalled at the sheer lack of evidence. Even when he saw Claw Shaw acquitted of all charges, Garrison then charged him with perjury for claiming his innocence during sworn testimony. A federal judge finally quashed the charge as a violation of Shaw's civil rights, for hounding him without just cause. The film postscript also claims CIA Director Richard Helms admitted Shaw was an agent. False-Shaw was admitted to have provided intelligence to the CIA as part of the Domestic Contact Service from things he observed while doing business in Europe. Thousands of businesspeople, diplomats and students did the same. There is no evidence Shaw was ever a paid CIA agent. In the film, the "source" for this was a French communist newspaper well-known to be a propaganda organ for Moscow. The KGB actually spread many of the early conspiracy rumors in an effort to weaken US morale, going so far as to fund authors who propagated them by using agents or front groups (without these authors' knowledge to be sure). The "Clay Shaw CIA Agent" story was just one in a series of false stories they planted.
"X" is presented as a Washington insider with deep roots, who has first-hand knowledge of the workings that led to Kennedy's murder. "X" is based to a degree on L. Fletcher Prouty (Prouty made most of the claims "X" states), a man with only a minor role in the Pentagon lacking such deep connections and, like Garrison, near-universally considered a crackpot even by other conspiracy theorists.
Kennedy himself is portrayed as some kind of uber-peacenik who would have prevented The Vietnam War and (somehow) ended the entire Cold War in his second term. In fact, Kennedy was a consummate Cold Warrior who got elected on a hawkish platform and actually escalated American involvement in Vietnam. Outside of the film, Stone acknowledges this, but claims that Kennedy had a change of heart during his presidency. Kennedy's actual policies provide no evidence of this change, but it definitely happened!
Unfortunate Implications: This movie portrays every gay person as degenerate sex maniacs. Author David Ehrenstein called Stone out for this in his review, and also pointed out that Jim Garrison was a homophobe who targeted Clay Shaw with little evidence, when Shaw was a respected and beloved figure in New Orleans and a friend of Tennessee Williams, with JFK tarnishing his reputation.
The Woobie: David Ferrie: Expelled from the life he wanted for being gay, becoming involved in shady deals almost by accident, and eventually getting in so over his head that he can't tell which way is up anymore. Whether you think his death was murder or suicide, you can't help but feel sorry for him.
Which is nothing compared to the Woobie he was in real life. Incidentally, in real life, he was as staunch a supporter of JFK as you'd ever find in New Orleans (he really did want to be a priest, and was thrilled that a Catholic had been elected president). And his death was from a Berry aneurysm, the culmination of years of poor health-there's no evidence that foul play was involved.