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.
YMMVs for the franchise as a whole: (for specific ones go to the corresponding season's YMMV page)
Audience-Alienating Premise: It's a Magical Girl series aimed at young adult men. Moe is de rigeur for most anime, but the cutesy imagery can be a turnoff for American (and some Western) audiences that don't look beneath the surface to the action series within.
Contested Sequel: With the exception of A's, which is considered an Even Better Sequel, any other entry into the main continuity has left the fandom polarised. It doesn't help that the author is constantly tinkering with the established formula in very unsubtle ways.
StrikerS caught flak for having a 10 year timeskip, thus losing most of the lolis. It moved the setting away from Earth and shifted focus from the previous main characters - demoting several to extras in the process - to a bunch of rookies and a lot more non-essential background characters. The Numbers cyborgs probably got the most heated debates among the fandom as to whether they were credible antagonists compared to the very powerful rivals from seasons one and two. They were also not as well-developed as previous antagonists, probably because there were so many of them. The third season was twice as long as previous seasons, but rather than using that extra time to develop its enormously expanded cast or give screentime to those characters inexplicably shoved out of the picture, the writers instead devoted most of the episodes to training the newbies and discussing military policies.
Sound Stage X was basically a continuation of StrikerS... with no characters introduced before that season making any appearances. People who were not fans of the new characters did not take it well.
ViVid was the first installment to shift from anime to manga, and a monthly one at that, so it already had a strike against it before it even started. Then it turned out it was a Lighter and Softer take on the series with plushy devices, no interdimensional incidents, Magical Girl tropes played straight and more lolis and loli fanservice than ever. It actually reads more like a shonen series with magical girls... and no real antagonists. And then it put the breaks on whatever plot it had going to do a lengthy Tournament Arc and introduce a bunch more new characters. People who liked the changes in StrikerS were disappointed, but in Japan where moe is the law it's the most successful entry in the franchise yet.
And then there's Force. If StrikerS broke the base, than Force Starlight Breakered what was left of it. Running concurrently with ViVid, it went completely the other way, all but ensuring that fans of one series hated the other and vice versa. It dropped most magical girl tropes altogether, introduced a bunch of new characters yet again, including an angsty male lead, which was the last thing anyone expected. It only keeps getting Darker and Edgier - innocent people are dying in bloody ways, antagonists are killing indiscriminately for fun, fan-favourite characters are being curb stomped left and right with powers that, in taking the previous season's Anti-MagicUp to Eleven, seem more than a little broken and the weaponsandarmordesignsarenow approaching Warhammer 40,000 levels of batshit insane. People think it's either a natural Sequel Escalation of the themes StrikerS started us off on and thus the most awesome thing ever or a Dork Age that never happened.
All of this is just from the main series. If we add the alternate continuities, we can also mention:
The Movie 1st, which was accused by some of being an unoriginal rehash of season one with half the plot and twice the explosions and cutting out pretty much anyone that wasn't Nanoha, Fate or Precia. Others liked it for exactly the same reasons.
The Movie 1st manga, which later turned out to have little to do with the movie and more in common with the light novel. It was widely decried for the perceived change in character of Nanoha - or Emoha as this version is known to the western fans - and generally trying to be too dramatic with the brutal fight scene between Nanoha and Fate that lasted for most of the second volume. And despite being an Alternate Universe that changed many things along the way, it still ended the exact same way as the original anime and the movie, leaving many to wonder what the point of it was.
The Movie 2nd A's was accused by many of butchering the lauded A's storyline. People complained about the changes such as: replacing Nanoha and Fate's reunion from Big Damn Heroes to hugging; having them completely defeated in the first encounter with the Wolkenritter; removing Yuuno from the battle; teasing a fight scene with Lindy that gets promptly aborted; Reinforce trying to kill Fate and Nanoha, without a good reason this time; Nanoha doing significantly less well against Reinforce; and of course, removing the Liese twins and the Graham subplot altogether.
The Fate/stay night crossover, which disappointed people who were expecting something serious and longer than a one-shot.
The Battle of Aces was generally well-received for shifting the focus back to the A's characters and the introduced Evil Twins of the main characters became popular enough to be included in the sequel, but even most of its fans admit that it was mediocre in terms of gameplay.
The Sequel to the above game The Gears of Destiny almost broke this trend. The game have a stronger AI, great amount of playable characters, and a good story with good character development. However the manga cast contributed next to nothing to the overall main story, and the ending used Laser-Guided Amnesia and removes all the Original Generation characters from the timeline until at least ViVid. It feels like they were trying to invoke In Spite of a Nail to make this timeline identical to the main one. It left the feeling of The movie manga all over again.
Ensemble Darkhorse: Despite suffering of Chuck Cunningham Syndrome, Yuuno is pretty popular by the fans, as he often appears in many fanarts and fanworks. In the latest popularity poll of ViVid, Yuuno manages to get the 13th place despite appearing only in a single panel.
Hilarious in Hindsight: Would you believe this was the prototype for the series. If you've watched the show for any length of time, the sight of Nanoha waving around that puny heart-shaped wand alone will be enough to make you crack up.
Just Here for Godzilla: Subverted. Before the first season's Growing the Beard moment, viewers were expected to just be there to see cute little Nanoha from Triangle Heart 3: Sweet Songs Forever in a strange alternate universe. They were quickly disproven when Nanoha got more viewers than the Triangle Heart 3 OVA. Ever since Nanoha became the perfect example of More Popular Spin-off, to the point where anyone looking for Triangle Heart 3 is probably just there to see Nanoha in a strange alternate universe.
Due to her Love Martyr status and stubborn refusal to hold any kind of ill will towards her abusive mother, Fate is often portrayed as a memetic masochist who loves to be wiped, electrocuted and generally punished. Needless to say this fits well with the merciless White Devil flanderization of Nanoha.
Due to her whole Defeat Means Friendship shtick, "befriend" has become an euphemism for "beat the living crap out of".
Rescued from the Scrappy Heap: As time passed, reception of Precia Testarossa has lightened, especially in presence of the much reviled Hückebein. First she got Woobie moments in the Movie 1st, then in Gears of Destiny her spirit made peace with Linith's, and finally INNOCENT showed what kind of mother she would have been had she not lost Alicia. Impressive, when back in the day, she really was the bonafide "most despicable, worst mom ever" with evil acts to prove it.
They Wasted a Perfectly Good Character: YUUNO. In a series so focused on how the ancient civilizations and technologies of the past are enormously impacting upon the present day, having an archeologist, scholar and librarian of ancient knowledge in the cast would seem like a great idea. If nothing else, Yuuno could have continued his roll as Mr. Exposition in StrikerS, Sound Stage X, ViVid and Force, considering that no one would be better qualified to explain about the Belkan Reunification War, the Sankt Kaiser dynasty, the Saint's Cradle, the Hegemon Klaus and his relationship with Olivie, Queen Ixpelia and the Mariage, and perhaps even the Bible of the Silver Cross and its Eclipse Virus.
Also the children are superpowered. One could argue they need to be given something useful to do, lest they find their own trouble, also that they're not in much danger; alternatively, there's so much danger to entire cities or even planets that you have to use every resource you can. Sound Stage X refers to a planet with 'real' child soldiers with guns, and IIRC that's portrayed as messed up and tragic.
More dissonance: not only is Chrono a 14 year old military officer (again, with the powers of Starman), but his mother is his commanding officer.