Contested Sequel: Primarily because this is the first series that steps away from magical girl elements and toward a more military setting, but also because some characters are pushed aside in favor of new ones, Yuuno and Chrono being among the most frequently mentioned. It also doesn't help that the girls are aged up and the setting has moved off of Earth, ensuring that there is very little of the familiar to fall back on.
It wasn't uncommon after StrikerS to ship Vivio with Lutecia (the only other person remotely close to Vivio in age who wasn't related to her in some way) or to age Vivio up and pair her with Hayate (most likely because Hayate is one of the few main characters without a 100% confirmed ship). This has died down a lot nowadays thanks to Vivid since now most everyone tends to ship her with Einhart.
It's not uncommon in some fan works with Ginga to either ship her with Fate or at the very least insinuate that she has a crush on her most likely thanks to Fate rescuing her when she was younger. It is downplayed however since Ginga wasn't that much younger then Fate when she was rescued and it's very likely the two would work together on cases so a romance is possible.
The TV version of the "White Devil Incident" in episode eight of StrikerS made a lot of people think that Nanoha had some sort of Post Traumatic Stress Syndrome from the timeskip between A's and StrikerS and that her reaction to Subaru and Teana's dangerous tactics in the mock battle made it look as if she wasn't fit to be training the two. The DVD version of the situation helped clear up any misgivings. She had more of a "disappointed parent" look on her face than the more Higurashi-like look in the TV version.
Just before her legendary attack in episode 25, she stomps on the floor, possibly to brace herself, but more likely simply because of how badass it makes her look. In the TV version, some dust is kicked up when her foot pounds onto the floor. On DVD that part of the floor is destroyed. Inexplicably, many people seem to prefer the second.
Various examples of QUALITY animation are fixed in the DVD releases as well.
Cinque of the Numbers is fairly popular, despite only appearing in three episodes and being the only one absent from the final battle.
Despite - or perhaps because of - her incredibly minor status, Sette is starting to gain popularity in some fanfiction circles. One popular topic is to expand on her fate - she is not in rehabilitation like the rest of the younger Numbers, but appears to be treated as less of a criminal than the older imprisoned Numbers, leaving open the possibility of her release.
Fanon Discontinuity: For some. Which is to be expected given the very drastic changes in setting, compared to the previous seasons.
Growing the Beard: The show is slow for the first ten episodes, focusing on training the new foursome and not very impressive battles against generic robots. Then Vivio comes along, and the plot and action kick in with force.
Hilarious in Hindsight: Lutecia Alpine's fan nickname ("Loli-Rider") now qualifies as this due to the Babylonia chapter of Fate/Grand Order releasing a younger version of Medusa under the Lancer class.
Moe: Reinforce II, Vivio and the younger Subaru seen in flashbacks. Even Adult Nanoha still qualifies as this.
Moral Event Horizon: Quattro crosses this when she brutally tortures Vivio and insults her mother Nanoha right in her face. If she didn't cross it then, she definitely did when she forced Nanoha and Vivio to fight each other. Especially with her line, "Now kill each other, like a good mother and daughter".
Never Live It Down: Nanoha's Blood Knight reputation was already around by the time of A's, but after her abortive brawl with Signum in the manga there was no going back.note Note that this is a coloured and enlarged, but otherwise completely unaltered panel from the canon StrikerS manga.
Straw Man Has A Point: Regius is one of the few people who distrusts Hayate for her criminal past, and even Auris suggests that he keep his opinions to himself. While the viewers and those close to her know she did nothing wrong during the Book of Darkness incident, he and much of the rest of the Bureau apparently heard a version of events in which Hayate accepted full responsibility, making his distrust seem more logical if ultimately incorrect.
Nanoha's near-death experience is very underplayed, although the belief that something like that might happen again is why she is hesitant to adopt Vivio at first, and she later resolves to make sure it does not happen again for Vivio's sake.
Regius's distrust could have segued into political intrigue and been expanded, but gets forgotten about very quickly.
Throughout the season, they keep comparing Nanoha, Fate and Hayate to the "Three Great Admirals" who created the TSAB, with the implication being that they would become the ruling forces for the Conspiracy Redemption. This notion is completely stomped on in the epilogue materials, perhaps because it would have interfered with Magical Record Lyrical Nanoha Force.
Tough Act to Follow: StrikerS is the first entry in the Lyrical Nanoha franchise to continue the story after the widely successful A's, which is almost universally considered to be the best entry in the entire series by fans, so this series had an uphill battle from the very beginning. Whether or not it lives up to the potential of the aforementioned season is a matter of debate.
Agito. The poor thing was used as a lab rat by mysterious scientist and it was almost completely broken when Zest and Lutecia rescued her. She recovered her enthusiasm and becomes a loyal Unison Device to Zest only to see him die at Signum's hands. Agito was taken under Signum's wing and they started to slowly develop close bonds and the little redhead eventually grow genuine feelings for the Blazing General. Came FORCE and she witness how Signum is near killed in front of her eyes while she's unable to do anything to help her beloved master. Life has been pretty harsh on this little device.