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.
Character Rerailment: In the comics, Gambit's characterization had been changed to a Self-loathingAtoner desperate to punish himself for his (morally blameless) role in the Morlock Massacre. This movie, however, reached back to the character's roots and showed him as competent, charming, handsome and relatively low-angst card-sharp who won a Cool Plane in a poker game.
Contested Sequel/Sequelitis: For many, it is a Narm-fest which flies in the face of the other movies' continuity (particularly rewriting a lot of back story from X2: X-Men United, the franchise's peak until X Men Daysof Future Past), ruins both Gambit and Deadpool, allows a lot of characters to make stupid decisions in the name of advancing the plot, and all for the sake of making another movie centered on Wolverine when the first 3 were essentially his show, anyway. For others, the continuity wasn't all that important, Sabretooth was finally given his due with some decent character development, the incorporation of some new mutants was interesting, and the whole thing is a fun action film.
There are also a number of fans who felt that the film was simply a poor rendering of Wolverine's origins that did not capture the true horror and brutality of what the Weapon X program did to him.
Continuity Lockout: The film could have used footnotes to explain the significance of its story elements. Since the Weapon X scene was so brief, it could have said "To learn more, please read Weapon X by Barry Windsor-Smith."
Wade Wilson. Not Deadpool, oh no, but critics and fans pretty much unanimously praised Ryan Reynolds as pre-experimented Wade Wilson.
Despite his short amount of screentime, Gambit has been well-received.
Fanon Discontinuity: There are some that prefer to ignore this movie because it was poorly executed and has a lot of continuity errors with the main series. The two movies that followed even ignored it (although The Wolverine briefly includes a scene of Origins in a flashback).
Real world instance: Fans had been clamoring for Gambit to appear in X-Men films since the first one. The public response from the directors and writers was, "If we include him, we want to make him integral to the story. We're not going to just throw him in there because he's popular." Come this film, Gambit is in, fulfilling a minor role which could be handled by any character. It really seems like the studio executives just thought, "Who's a popular character we haven't used yet?"
Also, the video game ends with Wolverine in a future with Sentinels. What happens in the end of The Wolverine?
Just Here for Godzilla: One review (sorry folks, it's in Hebrew) claimed that basically, the only reason to watch the film is because it has Wolverine kicking ass—and not even particularly well.
No Problem with Licensed Games: While not a brilliant game, the video game of the movie is a fun, gory, hack-and-slash with well-working gameplay mechanics, plenty of fanservice, and expanded plot points. In fact, the game seems to be more well-received than the movie it's based off of! (As the developers worked on the also-very-well-received X-Men Legends, Marvel Ultimate Alliance, the two most recent titles in the Star Wars Dark Forces Saga and Star Trek: Elite Force, this may not actually be surprising.)
Interestingly, it also ends on a cliffhanger/possible sequel hook that is completely unrelated to the film's plot.
One-Scene Wonder: Patrick Stewart’s cameo near the end elicited applause from some theater audiences.
Relationship Writing Fumble: The film is mostly about a heterosexual relationship, but the relationship between Wolverine and Sabretooth is too strong to be unintentional. While both characters repeatedly talk about how they're 'brothers', the constant Something Else Also Rises, playful flirting, eyeing each other, phallic symbolism, and grappling each other while yelling "Feels good, doesn't it?" kind of ruins the 'brothers' vibe. It's worth noting that the comic-book version of Wolverine's childhood featured a significant redhead named Rose as his first love interest. The first scenes in the movie are copied almost directly from the comic, except with a young Sabretooth in Rose's place.
Special Effect Failure: The effect used to depict Emma Frost's diamond form pops out for its low quality. Also, though Wolverine's bone claws were well done, his adamantium claws, particularly in the bathroom scene, inspired much derisive audience laughter. You'd think in a movie explicitly about a mutant with metallic claws, that would get more CGI attention than anything, especially when incarnations in previous films (by the same FX studio, even!) were pretty good quality.
They Just Didn't Care: The film's treatment of Deadpool. It honestly does feel like they were trying to piss the fans off.
It's made all the more egregious because Deadpool is primarily known for his snarky attitude and general savviness to the world around him. Removing BOTH of those traits is so perplexing that one wonders what the filmmakers were thinking in even including him.
To call the film's rendering of Wolverine's origin half-hearted would be an understatement.
Wade Wilson/Deadpool. After getting the chance to display a weary snarky persona, he's taken out of the film until the climax, where we see that Stryker has basically turned him into an Humanoid Abomination. With his mouth sown shut, essentially robbing him of the sole trait he had in the movie.
Comic fans had been calling for Gambit to show up in the movies since the first X-Men film. When he finally does here he's little more than a built-up throwaway gag.
will.i.am as Kestral in particular stands out. His passion for the source material is clear even when though movie is... troubled.
Uncanny Valley: The film features a cameo of Professor Xavier, which uses CGI to de-age him. The problem is, it was less-than-spectacular CGI and it just succeeds in making him look really creepy.
For those of you who haven't seen this film—he looks like Humpty Dumpty.
The same effect was used in X3 to de-age both Xavier and Magneto, but was much better-looking and a lot more convincing.
WTH, Casting Agency?: Downplayed with Liev Schreiber, who's about a foot shorter than Tyler Mane, as Victor Creed. He's excellent in the role and pretty intimidating, but it's still a tad jarring. Meanwhile Danny Huston, the actor playing the young Stryker, is like a foot taller than Brian Cox, who played Stryker in X2. Even barring height, Cox and Huston look nothing alike.
The Woobie: Teenaged Cyclops. Poor little guy. Awwwwwwww.