Growing the Beard: The first three episodes / first sound stage of the anime are arguably mostly standard Magical Girl fare and while not awful aren't anything special either especially since the show is still finding its roots and as such suffers from Early Installment Weirdness. Once Fate is introduced and the mythology of the show starts to move more towards its Space Opera / Gundam roots, the series becomes considerably more interesting and unique.
He's Just Hiding!: More then a few fans don't buy that Precia just fell to her death at the end of the season and hope that she will return one day for some well deserved payback at the hands of Nanoha and Fate.
Moe: Nanoha and Fate both fit this trope perfectly. In fact, Nanoha even won the 2005 Saimoe Tournament, and until recently she was the winningest character in Saimoe history.
Moral Event Horizon: Precia whipping Fate for not bringing enough Jewel Seeds back, despite bringing half a dozen and working constantly despite the risks to her health from everything she's doing.
The Woobie: Poor Fate, again. She just wants to please her mother, but nothing she does over the course of the series is ever good enough for her and she gets horribly abused no matter what she does. Towards the end of the series, even after she finds out that she was just an Artificial Human modeled after Precia's real daughter Alicia, and that Precia never thought of her as her daughter, she still tries to make reach out to her.
Jerkass Woobie: Precia in contrast to the original incarnation. She's just as cruel to Fate as in canon, but it's revealed that not only was she a loving mother who wanted to spend more time with her daughter, but she tried to prevent the premature launch of the reactor that caused the meltdown that killed Alicia, and the companion manga shows just how painful it was for her, especially with her cradling Alicia's lifeless body in her arms as tears are streaming down her face. In her final moments, as she's falling to her apparent death, she appears to finally understand Alicia's desire for a little sister and regret her actions.
Pandering to the Base: Nanoha's transformation was arguably more fanservice-based, and Fate got a transformation sequence of her own. Bardiche and Raising Heart both got new looks, as well. Conversely, there's a lot of background information that didn't make it in the movie, which ONLY fans of the series would know about.
Nanoha is considerably more angsty in the movie manga, and some people believe she falls into this at times. For example, while at the end of the Jewel Seed case in the original anime, she was mostly satisfied with how things turned out but somewhat worried about Fate, she believes in the movie manga that she was unable to help anyone at all. This has lead to the Fan Nickname "Emoha" for this version of Nanoha.
In fact, the manga's story is quite a bit more gratuitously angsty in general. Fate doesn't recover from her Heroic BSoD in time to either team up with Nanoha or confront Precia, Chrono blames himself for the trauma that Nanoha and Fate went through, the general consensus among the Arthra's crew is that the jewel seed incident was a lost cause, and even freaking Raising Heart angsts when it thinks that it's given Nanoha faulty combat advice.
The Woobie: Linith. Her plight is even more poignant in the movie manga, as she reveals that she wanted to take Fate and Arf away from Precia, but knew that doing so would hurt her, and realized that Precia and by extension, herself as Precias familiar had no more than two years to live. She thus did her best to ensure that Fate became strong and had a good relationship with Precia, and told Fate that she hoped she would find a good friend.
While Fate was already The Woobie, this was amped up significantly in the movie mostly through little moments like wistfully watching a mother and child interacting on the street, or glancing sadly at the wrecked cake she tried to offer Precia. With lots of lingering shots of her large, soulful eyes...