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.
UQ Holder inherited quite a bit of Negima's base, which is split between being pissed this isn't a more direct sequel, happy to see a new setting uncluttered by Negima's Loads and Loads of Characters, and those still mad that Akamatsu ended Negima so abruptly as a Writer Revolt against the publisher, and then went back to them anyway.
The fans are also rather torn down the middle on the topic of Evangeline's new character design and personality, some to the point of They Changed It, Now It Sucks.
The revelation that Touta is a Konoe and apparently Negi's grandson brought back some of the old Ship-to-Ship Combat. A lot of fans speculated that this meant that Negi ended up with Konoka, which pissed off both Konoka/Setsuna fans and fans who wanted Negi to end up with pretty much anyone else. Though much of the fire of this debate died out when people realized that the timeline is set far enough into the future that it was possible that Negi's child could have married Konoka's child.
Touta himself also induces his. Power-wise he more-or-less takes up where Negi finishes. Magia Erebea is the stuff that allowed Negi to go stand equal to the likes of Rakan/Fate/Lifemaker. He gets it as a regular power-up. His generic Shounen Idiot Hero character hurts him when compared to Negi.
Touta and Kuroumaru have plenty of Ship Tease, but it's quite hard to tell if it is Ho Yay since Kuromaru is still genderless.
Karin is violently jealous of Touta due to his closeness to Yukihime.
Fate continues to display a heavy amount of Ho Yay towards Negi. Touta even calls him on it.
Ship-to-Ship Combat: A funny example between those who ship Kuroumaru with Touta. Since Kuroumaru is genderless till sixteen there are those who would like to see him become male while there are others who would prefer him to become female. A smaller party would prefer him to stay genderless, which may be possible since, as an immortal, Kuroumaru might not age.
Viewer Gender Confusion: It's not quite clear whether Shinobu is a girly boy or a tomboy Bokukko, though most readers assume the latter due to being an expy of two Shrinking Violet girls from Akamatsu's previous works, but with the introduction of Kuromaru who hits the readers hard with this trope, many are not trusting their own judgment.