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, reaches back to the character's roots and shows him as a competent, charming, handsome, and relatively low-angst card-sharp who won a Cool Plane in a poker game.
Contested Sequel: 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: Days of Future Past), ruins both Gambit and Deadpool among other characters, 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 three were essentially his show, anyway. 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. 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.
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, pre-experiment. Critics and fans pretty much unanimously praised Ryan Reynolds as Wade, and it was what gained Reynolds a shot in the character's solo film.
Despite his short amount of screentime and differences with the character, Taylor Kitsch's portrayal of Gambit was well received. Kitsch himself requested on countless occasions to be cast again in any other X-Men film, but he wasn't brought back for the oncoming movies, which will feature Channing Tatum. Supposedly.
Fridge Brilliance: The previous X-Men films established that head injuries (blunt impacts or gunshots) will knock Logan out, while Logan easily shrugs off a headshot from Agent Zero. Considering Logan establishes that his healing factor was deteriorating due to the Adamantium, it makes sense for Logan to be immune to such injuries during a period where he hasn't been bonded to the metal for too long yet.
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?"
"Revenge Painting", referring to an incident involving former Fox CEO Tom Rothman re-painting a set behind director Gavin Hood's back, is a term used to describe the copious amounts of Executive Meddling that went into the film.
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.) Ironically, the story of the game works rather well when it's not trying to follow the plot of the movie. Interestingly, it also ends on a cliffhanger/possible sequel hook that is completely unrelated to the film's plot. Ironically, though, it sets up X-Men: Days of Future Past fairly well except for the future Continuity Snarl that is Trask.
Practically everyone agrees on the sheer awesomeness of the opening credits scene featuring Logan and Victor fighting throughout the wars.
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.
Retroactive Recognition: Runs into issues with the above, of the "How the heck did Troye Sivan grow up to that?" variety.
The Scrappy: Wade Wilson after he becomes Weapon XI, primarily due to the fact that the Merc with a Mouth gets his sewn shut. This, coupled with the In-Name-Only handling of the character, did not sit well with fans, even though his fight with Wolverine, Sabretooth, and Gambit isn't terrible. Oddly enough, this is one of the few cases where a character is The Scrappy and an Ensemble Darkhorse in the same work, as Wade is considered the highlight of the movie before he's transformed.
The effect used to depict Emma Frost's diamond form pops out for its low quality.
Though Wolverine's bone claws are 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.
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. His mouth being 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.
They Wasted a Perfectly Good Plot: So we have the opening scene, which establishes that Logan is indeed older than he appears to be, having been born in the 1800s. So no doubt the movie will take advantage of this immortality-based storytelling device and make the movie about Logan's life leading up to the implantation of his adamantium skeleton, right? Nah, let's just relegate that potentially interesting story into a three minute opening credit sequence in favor of a plot that will ultimately become irrelevant due to the inevitable amnesia Logan will suffer from.
Uncanny Valley: The film features a cameo of Professor Xavier, which uses CGI to de-age him. The problem is, it's less-than-spectacular CGI and it just succeeds in making him look really creepy—kinda like Humpty Dumpty. The same effect was used in X-Men: The Last Stand to de-age both Xavier and Magneto, but was much better-looking and a lot more convincing.
What an Idiot: Okay, Wraith. Try to take Sabretooth on. Never mind the fact you're trying to punch a man with an absurd Healing Factor to death. Sabretooth getting a One-Hit Kill was probably a mercy because every punch Wraith landed probably would be doing more damage to himself.
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.