Contested Sequel: Largely because of the Darker and Edgier atmosphere, move away from Magical Girl tropes, new main character, and largely unsympathetic villains who defeat and severely wound Signum and Hayate. A good number of people have pointed to apparent lapses in the worldbuilding, raw writing and the artists difficulties with portraying dynamic fight scenes as a sign of a general drop in quality. Continuing questionable decisions and completely out of touch ideas of who the fanbase cares about seeing in a Hot Springs Episode mean the future is not bright, especially with the "temporary" cancellation.
Crack Pairing: Signum/Cypha. It's almost exclusively based around Signum being dominated and humiliated. It probably started as a thing to troll fans with, but since it became obvious that Signum would live through Force, it seems to have been jokingly accepted by the fandom, kind of like Mami and Charlotte.
Fridge Logic: Mariya uses live ammo in a fight against Bureau agents on the Mid—which is kind of a Big Deal, since live ammo is exactly the kind of mass-based weaponry the Bureau is supposed to crusade against. Yet nobody seems particularly interested in finding out where a lowlife crook like herself obtained such quantities of mass-based munitions in the heart of the Bureau's domain. Granted, she doesn't have an actual gun, but bullets usually come from the same sources as firearms...
In Chapter 20, Shamal asks Vivio if she wanted to join in the mock battle with Thoma and Signum. Why would she make that suggestion given how dangerous Thoma or Lily's Eclipse powers would be to Sacred Heart/Chris if Vivio tried to fight either of them? Nanoha, on the other hand, suggests Vivio to not get involved.
Heartwarming Moments: Signum and Agito's interactions in chapter 3. Their affection for each other is quite subdued (as befits a Belkan duo on a job), but seeing the stoic knight smile for her partner and Agito finally finding happiness in service of a worthy Lord is Squee-inducing. Which makes their utter slaughter by Cypha just four chapters later all the more jarring.
Hilarious in Hindsight / Ascended Meme: Nanoha gets a new getup in this that actually makes her look like a Gundam bringing the "Nanoha is really a Gundam disguised as a magical girl" bit full circle.
Thoma has drawn a lot of fire for being a very typical, male, angst-ridden main character with a Story-Breaker Powerpulled out of nowhere that can beat out the established and well-developed main characters of previous seasons with little effort. His latest comments to both Signum and Cypha, where he wishes both the hero and the psychotic good luck and tells them to do their best before they fight, suggest Thoma has serious issues.
Cypha's caught a lot of flak for handing Signum her first real defeat, and for being kind of a bitch about it. When it was announced that Gears of Destiny will feature Force characters, many were hoping Cypha would be included, so they can beat the crap out of her.
Curren probably beat Precia's record for instant hatedom, considering the chapter with her first appearance wasn't even translated yet and people already wanted her to die. The reason? Debuting by instantly impaling Hayate in the back, just as she was finally about to do something awesome.
While he is mentioned in Replacement Scrappy, Thoma isn't liked for his behavior crossing into the What an Idiot! territory and losing characterization into becoming what is seen as an idiot who keeps overlooking the behavior the Hückebein constantly exhibit. What's worse is that he is borderline useless in combat and is overshadowed by Isis and even Lily, combined with wasted character development potential.
Most people don't really like the AEC Equipment much. They prevent the heroes using magic in a setting that has previously been about high-powered magic, they usually don't work, and anyone with a Strike Cannon rather than a personalized weapon gets taken down like they were a Mook regardless of what they were treated like in any previous version of Lyrical Nanoha.
Thoma became a fugitive from the TSAB by breaking into the lab, stealing the Divider, and escaping with Lily. This might have led to Subaru weighing her bond with Thoma against her duty to arrest him, as well as Thoma fleeing from the Bureau while having the Sympathetic P.O.V., but Thoma eventually loses control of himself to the Eclipse, and it becomes about having to try to get through to him, rather than him trying to protect Lily and escape the Bureau.
Force in general could have been presented straight as about the conflict between the refusal of most of the main characters to kill and the fact that the only solution to the Hückebein appears to be killing them.
Signum gets chopped up, and Vita gets taken out like she's a Mook, but they take it in stride. Which is more than slightly out of character. Every time someone has threatened Hayate's life previously, the Wolkenritter have treated them as mortal enemies. In Force, they don't seem to care nearly as much.
Signum and Cypha's rivalry. With such a rocky start and looking at the Blazing General's Blood Knight tendencies as well as the eye-patched rogue's animosity to fight strong foes one would think an instant comptetitiveness would emerge between the two. Instead Signum abides to her duty almost ignoring everything else while Cypha didn't really seem eager to pursue another fight (aside of some passing remarks at Signum's good swordfighting skills), she even fled their second encounter without a care. Hopefully, their feud and mutual grudgingly learning will be more fleshed out if FORCE's hiatus ever gets lifted.
Unintentionally Unsympathetic: In interviews the author has seemed genuinely shocked that people do not find the Hückebein sympathetic or likeable, particularly Cypha. While their lot may kind of suck, they're still mass-murdering sociopaths who treat all attempts to reason with them as an excuse to commit more horrific violence.
Viewer Gender Confusion: Until his profile came out, nearly everyone was convinced that Fortis was female. With his large eyes, dress-like robe, and feminine hairstyle, it's an easy mistake to make. Ironically, fortis can be translated from Latin as "manly".