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.
Adaptation Displacement: The original novel by Mario Puzo is less well-known than the films. The way that the films are titled "Mario Puzo's The Godfather" were actually an attempt by director Francis Ford Coppola to avoid this.
Award Snub: This might seem churlish in light of the fact the first two movies each won Best Picture and numerous other Oscars besides (though Coppola lost Best Director for the first one to Bob Fosse, he won for the second one), but amazingly enough, Gordon Willis' seminal camerawork in the first two movies wasn't even nominated. Think about that.
Al Pacino's performances as Michael Corleone in Parts I and II and especially Part II are considered to be among the best performances in film. Yet, he received no Oscar for either one. He was even nominated in the wrong category (as Supporting Actor) for Part I when he was obviously the main character.
A more jarring example: three actors from the first movie were nominated for Best Supporting Actor. They all lost.
To Joel Grey for Cabaret, though.
Additionally, three actors were nominated for Part II, but John Cazale wasn't among them, even with Fredo taking on an emotional crux in the latter portions of the film.
Badass Decay: When Sollozzo has Tom held captive, he says that Vito and Luca would never have fallen for the ploys used if it were years earlier, trying to suggest that they've gotten soft.
In the book only, we are Informed that Fredo was a tough guy who just took his eye off the ball during the attempted assassination of Vito and decayed after running the Family business in Vegas for a long time. None of this shows up in the movies, where he comes across as an incompetent boob. Given that Fredo's toughness was certainly an informed ability, perhaps that was for the best.
Big Lipped Alligator Moment: There was a quite lengthy subplot in the original novel about one of Sonny's mistresses who went out to Hollywood, became friends with Johnny Fontane, and eventually fell in love with a plastic surgeon who performed reconstructive surgery on her vagina and then married her. Francis Ford Coppola later said he was so disturbed by this portion of the book that it almost put him off filming it. Part III ignores this entirely by introducing Vincent, who is the same mistress's son (the book makes a point of saying Sonny never knocked her up before he was killed).
This subplot tied into a bizarre string of borderline poetic passages going to great lengths to romanticize Sonny having an abnormally large penis (to go with his girlfriend's abnormally large vagina), with other characters making cracks like "Sonny's cock is so large prostitutes charge him double!" and "Sonny's cock is so large his wife's glad he's having affairs!" Understandably, this was cut from the film as well. (Although, in the background of the wedding scene, you can see an allusion being made to it...)
Contested Sequel: The Godfather Part III. Opinions range from "absolutely terrible" to "not terrible, but not as good in comparison to the two masterpieces that preceded it". Some people contend that Part III would be a great movie, if not for the comically bad performance of Sofia Coppola as Michael's daughter. It would have also been nice to have Robert Duvall back as Tom Hagen.
There are some who consider it just as good as the first 2; this video essay makes an argument for how the third film works if seen as the epilogue to the first two, as Coppola and Puzo originally intended.
Do Not Do This Cool Thing: As long as you don't look too closely, the mob life looks very attractive when you can live it like Michael and Fredo and the rest. Even all the shady stuff - killings, fights, wife abuse, prostitution, drugs, animal cruelty, and double parking - seem so appealing.
Ensemble Darkhorse: Luca Brasi is only in the first film for a few minutes, and has less than five minutes of screentime. He's also very popular, and in the first video game, was featured prominently as a sort of mentor.
Even Better Sequel: This series has what most critics consider to be the Most Triumphant Example; Part II vs. the original.
Fight Scene Failure: When Sonny beats down Carlo, one of his punches very obviously misses by a mile, but comes with an impact sound effect and reaction. Ironically, James Caan really did injure Gianni Russo during the filming of this scene.
Genius Bonus: The establishing shot of the meeting between Vito and the heads of the other five families shows that it is being held in the Federal Reserve.
Hype Backlash: Because so many people consider it to be the greatest movie of all time, it's inevitable that some people will walk away from it wondering what the big deal is.
Memetic Mutation: "An offer he can't refuse", the horse's head, "the day of my daughter's wedding", "may your first foist child be a masculine child", the first known use of the phrase "badabing!", and many more.
Misaimed Fandom: More than a few people have, when discussing the film, referred to Michael as the ultimate Bad Ass. Smart, powerful, decisive, etc. That is not the point of his character arc. His story is a tragedy. Real-life mobsters are huge fans of the trilogy.
Part II's Moral Event Horizon is much clearer where Michael has his own brother Fredo killed for unwittingly betraying Michael to Hyman Roth. Even when it's become obvious that there was no need for the killing. It's so painful that Part IIIcan be viewed as Michael's attempt to atone for the sin of fratricide by seeking salvation allying with the Catholic Church.
Fredo, though, at least had done something to deserve it. Arguably worse, and the starkest illustration of the moral emptiness at the heart of Michael's pretensions of family, is the casual murder of the prostitute to frame Senator Geary. She just happened to be the girl with him that night and her death was good for business.
Carlo viciously beating Connie in order to draw Sonny out and have him killed.
Never Live It Down: The notion that Frank Sinatra used the mob to get his role in From Here to Eternity (that he got his Academy Award for) is not based on any evidence from Real Life, but this book and movie. Incidentally Sinatra claimed he would have played Vito had Coppola asked him, and was originally cast as Don Altobello (who was later played by the man Sinatra replaced in 'mEternity'm, Eli Wallach
Paranoia Fuel: Woltz has this realisation in the novel after that (in)famous scene, recognizing that if The Mafia could sneak onto his grounds and do the deed they did... In the sequel novels written by Mark Winegardner, when Tom Hagen is obligated to pay Woltz a visit several years later, he finds that much of the tasteful statuary and landscaping on the property have been removed and replaced in favor of greater visibility and security, giving the house a stark, almost fortress-like feel.
Tear Jerker: Toward the end of Part I, after Vito and Michael have had a final consultation, Vito is hit by an overwhelming wave of sadness, as he looks back on all the things he's done in his life. He says he Did What He Had To Do, and he has no regrets. Well, except one: that it's Michael who must now carry on the family business. He confesses that he once had hopes that the Corleones could be legitimately powerful, maybe even have had a mayor or a senator in the family... and that he had hopes that Michael could have been that. The broken way he says to Michael, "I never wanted this for you," speaks volumes.
Fredo is this to a lot of fans for being such a weak, incompetent, pathetic character, and his betrayal in the second movie doesn't help.
Mary Corleone. Sofia Coppola's performance as Mary in the third film is hated by nearly all. Compounding the issue is the apparent nepotism of her casting. She was actually cast only because Winona Ryder backed out at the last minute and there was no time to get another actress. Sofia fared MUCH better as a film director.
Demonic Spiders: Damn Tommy gun and shotgun mobsters will tear you a new one for a lot of the game if you're not careful.
Disowned Adaptation: Francis Ford Coppola did not approve of the game, accusing its makers of profiteering off of his work.
It's Easy, so It Sucks: A charge often leveled at the sequel. Players often didn't bother with the "hunting the rival family's made men" sidequests because the benefit was negligible when it came time to take down the family compound. Elite Mooks, up to and almost including the family Don, were almost indistinguishable from ordinary buttonmen.
Player Punch: It seems like nearly everyone you know ends up getting killed by other mobsters, or betraying you and then getting killed by you. Luca Brasi, Paulie Gatto, Frankie, Sonny, Monk, Tessio, and Jaggy Jovino (and Sergeant Ferreira in the Wii version). YMMV because you never see these characters outside of missions anyway, so it's hard to get attached to them. Still, you gotta give the game some credit for trying.