Accidental Innuendo: In the first act of the movie, Hinata goes to Naruto's house to present him with a red scarf. However, her stomach growls, prompting Naruto to invite her inside. In Japan, it's highly inappropriate for a guy to invite a girl up to his room alone if they're not a couple, and Naruto and Hinata do not become an Official Couple until the movie's climax.
Adorkable: Most of Naruto and Hinata's interactions throughout the movie
The whole premise of the movie, which basically brings one of the longest, most intense Shipping Wars in anime history to an end. If you're a shipper, depending on which pair you support, this movie is either your wettest dream or your worst nightmare. And let's leave it at that.
Albeit to a lesser degree, this film was even controversial among non-shippers. Some are annoyed that the film even exists, since they feel it retroactively shoehorns romance into Naruto as a character, even though it was never a big, or even secondary aspect of the franchise. Others don't mind it, since they feel it fits with his other character traits without undermining them or even modifying them. Some people even thought it a better finale to Naruto than the actual climax of the manga.
Other than that, a few people were quite upset that Sasuke was Demoted to Extra in this film. On the flip side, other people were OK with it, since this is supposed to be Naruto and Hinata's love story, and unlike Sakura (whom Naruto previously had a one-sided shallow crush on up until Chapter 469), Sasuke was never part of that particular equation. Yet more people very much appreciated it, since Sasuke is such a Base-Breaking Character himself.
Captain Obvious Reveal: Hinata wasn't really leaving Naruto for Toneri, to the surprise of nobody but Naruto himself.
Common Knowledge: The Genjutsu scene in which Naruto sees how Hinata has always stood with him has been criticized by detractors of the movie as going against the "established lore of Naruto being immune to Genjutsu". In reality no, Naruto is not immune to Genjutsu even after getting into good terms with Kuramanote It was shown that he was vulnerable to the IT, which is why he, Kakashi and Sakura had to be shielded from it by Sasuke's Susanoo. What was actually said was that when a Jinchuriki who has control over their Biju and is in good terms with it, falls under a Genjutsu, its Biju would act as a partner and snap them out of it. The simplest explanation is that Kurama simply choose not to snap Naruto out of it seeing that his life was not in danger from a benign illusion, which is why Naruto was snapped out by his human friends instead.
Even Better Sequel: Shipping wars aside, many consider this movie an improvement compared with other Naruto movies (which are often labeled as "villain of the week filler movie") for having a better (and canon) story which explain better the Naruto/Hinata relationship and a better animation.
The main conflict is about the Moon losing its orbit and falling to Earth, a chapter of Kishimoto's next manga Samurai 8: The Tale of Hachimaru would deal with stopping a shattered moon from falling into its planet.
Jerkass Woobie: Toneri does a lot of terrible things, but it's easy to see why he turned out the way he did given that he was raised to believe he had to cause the end of the world and spent years in isolation with nothing but his puppets. And even after Naruto saves him, Toneri learns that the mission he family gave him and he devoted his life to went against the will of the ancestor he admired. Toneri feels so terrible he decides to stay on the moon, alone, blind, and without any of his puppets.
Les Yay: While the movie is about Naruto and Hinata becoming a couple, it doesn't stop Sakura's Cool Big Sis role from having this Hinata.
Misblamed: Some guys from Studio Pierrot openly admitted being Hinata fanboys in a omake many years ago and constantly give her extra screentime in the anime to the detriment of Sakura. It came off as no surprise that certain fans fell on them like vultures on a corpse when they discovered that they were not only animating this movie, but writing the script. However, Kishimoto has repeatedly stated that hooking up Naruto and Hinata was entirely his idea, that Hinata was always going to be Naruto's main love interest, and that Naruto/Hinata had been planned since the early stages of the manga. Kishimoto also joined the writing staff to create the final scriptExplanation Specifically, he was chief story supervisor for the first time ever on a Naruto film, meaning that he was heavily involved in the production of the film because he exercised direct and complete editorial supervision over the script so that this movie was included in the canon of the manga, rather than being an alternate continuity like all of the films that preceded it.
Some people think that Toneri looks too silly and poses too weirdly to be a threatening villain. A particularly egregious example is when the sealed Byakugans from the destroyed Tenseigan start amassing over his body. He just looks like a giant marshmallow.
A lot of fans couldn't stop giggling during Naruto and Hinata's running through the moon-portal, since it looks like a cheesy "run through the meadow" cliche.
During his final Armor-Piercing Attack to Toneri, Naruto, while he is holding the remains of Hinata's scarf, talks about how it takes time to knit a scarf and properly convey one's feelings. The cheese levels are off the charts!
No Yay: Toneri's Villainous Crush on Hinata. It's disturbing from the start with Toneri's state of mind, but then towards the climax he turns her into one of his puppets and forces her into an elaborate wedding dress with the implication that he stripped her naked.
Despite being heavily featured in promotional material, Sasuke only makes two appearances in the actual movie, and is especially badass in his second, partly because said appearance involves his only line of dialogue.
Rock Lee, whose one scene in the film features him punching a meteor in half.
Sasuke/Sakura vs. Naruto/Hinata. Some vocal Sasu/Saku fans are displeased by the lack of Ship Tease and actual content (like Sasuke wandering even after two years) and decided to declare the movie as Fanon Discontinuity. Considering the actual canon status of the movie, it didn't go well with Naru/Hina fans. To this day, passive aggressive remarks on movie are still present in SS fandom.
While the film was successful in that regard, thanks to Sasuke's Demoted to Extra status, the same couldn't be done for Sasuke and Sakura. Although a few key lines and shots heavily imply that they also had to work things out somewhere down the line before they finally got together. We just haven't seen it...yet.
Hinata gets hit by a vision that reveals to her that she is the only one that can destroy the Tenseigan and subsequently save the world. She doesn't know where the Tenseigan is located but she knows that Toneri is going to eventually come to pick her up in order to take her to his castle and marry her because he believes it's his destiny. You'd expect: She confides this bit of important information to somebody on her team, preferably the commanding officer with an IQ of over 200. The group then forms an effective plan in order to trick Toneri, track down and infiltrate his castle, locate and destroy the Tenseigan, save Hanabi and prevent the world from being destroyed. Instead: She remains completely silent and opts to make a scarf instead until Toneri shows up to pick her up. She goes on to attempt to locate and destroy the Tenseigan alone in a fortress surrounded by enemies. Result: Naruto gets seriously wounded and his heart gets broken thinking that Hinata betrayed him and stopped loving him. He then goes into a four-day Heroic BSoD giving up on everything. Meanwhile, Hinata gets caught red-handed by the Big Bad trying to destroy his Weapon of Mass Destruction, and she gets turned into one of his puppets. And THEN it turns out that her power alone is not enough to destroy the Tenseigan anyway. Really, it was only because of a bit of Contrived Coincidence that the world didn't get destroyed.