There isn't anything noticeably wrong with any character's hats, such as they are. Maybe that reviewer had a grudge.
The story is thus:
There is a planet, called Earth by the locals, with a pre-magic civilization hanging on the edge of the leap to post-scarcity, where an unremarkable wheelchair-bound schoolgirl named Hayate Yagami is given one of the most dangerous Lost Logia in the multiverse.
Inside the Book of Darkness are four immortal weapons, artificial warriors, horror stories of Ancient Belka. But, shaped by the will of a lonely young girl, they become people. For a time, they are happy together, but Hayate's health is now tied to the Book, and the Book hungers. Left alone, the Book will slowly paralyze Hayate, until she dies of suffocation or heart failure.
Believing that sating the Book will save Hayate, the four knights deceive her for what they believe to be her own good, hunting magical beasts and mages; defeating them, and then ripping their souls out surgically removing their linker cores to feed the Book.
Meanwhile, another young girl, a powerful mage named Fate, has completed her mandated rehabilitation and is returning to Earth with her new adopted family, the Harlaowns. She reunites with the titular Nanoha Takamachi, and tears and hugs and smiles are had.
Of course, being the two most powerful mages on Earth by a fair margin makes them obvious targets for Hayate's knights. A spectacular battle rages across the city of Uminari. Nanoha and Fate are defeated.
Thus begins the investigation, and the nigh-happenstantial meeting between Hayate and the other two girls.
It all comes to a head, the building tragedy masterfully revealed: there was never any saving Hayate, for the knights. The Book was going to kill her no matter what, and her knights have been hunting and hurting people behind her back for nothing. The Book itself "wakes up" and possesses Hayate, transforming her and using her to re-absorb the broken knights and carry on the hunting. It is here that it is revealed that there was a fifth knight all along, fighting to protect Hayate from within the Book. Her name is Reinforce, and she was the Unison Device upon which the Book was originally based.
But Nanoha and Fate aren't down and out, not yet. They've healed, they've recovered, they've learned, and Nanoha faces the avatar of the Book in single combat, in a spectacular battle that destroys a continent of Exclusion Barrier terrain. Fate hacks into the Book, and struggles with its mental defenses, her deepest hopes and fears laid bare and used to tempt or torment her, in an attempt to free Hayate. And ultimately, they both succeed.
Hayate is separated from the Book, now ascended to her own power, and what's left of the Book turns into an extradimensional self-replicating death swarm in desperation. The three girls wrangle the cosmic horror and blast it into orbit, where the dimensional cruiser Arthra (the same make as the one Verity is on, actually) captained by Fate's adopted mother Lindy, deploys its primary weapon and obliterates the planet-eating swarm before it can eat any planets.
Hayate's first four knights get revived, but Reinforce gets a tear-jerking death scene. Hayate cries in Nanoha and Fate's arms, but that very act is a seed of hope for the future. (Indeed, there're production photos during the credits showing the real Hayate, Nanoha, and Fate, in their late teens, posing happily together; they look the same as the movie versions, only older: there is a note that they gave permission to use their true likenesses rather than the actor's faces.)