I liked it, although I understand its reception has been hot and cold. It's fairly serious, set in a world with terrorism, international espionage and magic-based technology. I could imagine someone wanting it to be livelier, faster-paced or to have more colourful characters, but for what it is, I think it's in excellent control of itself.
It's set in the year 2095, after a century in which magic has been so exhaustively analysed that it's inverted Clarke's Law. You don't cast spells with a magic wand. You program it like software, although there's still old-fashioned magic that hasn't yet been computer-processed. Spells are fired from guns. One of the protagonist's research projects is about magically operated nuclear fusion reactors. Furthermore, there's also a century's worth of future history and politics, with climate change, a population crash and World War Three starting in 2045. People with magical talent are a scare natural resource and countries have tried to restrict their outward movement. (Inward is fine.) The world still has scary regimes, e.g. the Great Asian Alliance that's basically China after conquering most of Asia. Japan's still basically the same, but it's one of very few countries in the world that's neither broken up nor been absorbed into part of an empire or federation.
There's lots of information about all this in the Yoku Wakaru Mahouka DVD specials, by the way. They're only three minutes long, but invaluable for learning about the laws of magical physics, how technology fits into that, world politics, etc. There are things I learned from those that I'd missed in the TV series, e.g. the shortage of magicians for teaching. I made the mistake of watching these after I'd finished the main show, but I'd recommend watching them first. (The anime's based on a series of light novels, by the way, which often have more background detail than an anime's willing to tackle.)
I enjoyed all that. I loved the juxtaposition of writing a computer program for Shinto-based spirit magic. (There are other "magic turned into science" anime out there, e.g. Chaika the Coffin Princess, but not quite like this.) You get hackers, just as in real computers, and the reason for a hostile military operation might be access to a data warehouse.
There's other good stuff too. The show's well paced, especially compared with overstuffed shows that squash four novels into twelve episodes.
The fight scenes are strong too. This isn't an action show, but it's no holds barred when things do get ugly. Magicians are seen as weaponised humans, so it's plausible for our school-age heroes to be taking down military targets. (A couple of them are also current or former soldiers and have battlefield experience.) It's cool to see a terrorist assault team discovering that they're fighting a schoolboy with ninja training, magic spells and the ability to pull your limbs off your torso. I'm not normally too fussed about action scenes, but Madhouse is a top-notch studio and what we have here is very good indeed.
The protagonist is overpowered. Tatsuya Shiba is a schoolboy genius and super-soldier with ninja training who can invent things the world thinks are impossible, see through walls, analyse his opponents' magic in real time and beat any opponent in combat. He scored 100% on the school's written entrance exam. He failed the much more important practical exam, because he's bad at... um, something really important for magicians that in practice doesn't slow him down much. He's outrageously brilliant at everything. Then, in the finale, we learn that he has additional powers that make him a combination of Jesus and Shiva, Destroyer of Worlds. So... yeah. It's hard to imagine story continuations that could challenge Super-Tatsuya, although the original novels are still going.
Some fans can't take Tatsuya. That's understandable, but I quite liked him. There's also more to the show than just him and he's not overshadowing his friends. Besides, Tatsuya has other problems, e.g. being used as a minion by his scary family and having had his emotions burned out. (If you want to find out why, either read the books or wait for season 2 of the anime. Emotionless characters are common in anime and can feel like audience identification heroes for autistic otaku.) Tatsuya is also obsessively fair-minded, will put himself to almost unlimited trouble if asked politely and hates favouritism even when he'd benefit. We can forgive a bit of cold-bloodedness.
The show's other potential problem is Tatsuya's sister, Miyuki, who's elegant, modesty, beautiful and disturbingly into her brother. They're deeply inappropriate together. It flusters the other characters in the show, let alone the audience. Nothing actually happens and it seems that Tatsuya's sister complex is partly just him teasing people. Miyuki, though, is serious. It's very hard to see her feelings as just platonic. Threaten Tatsuya and she'll freeze you into an icicle. She's capable of freezing everything in sight, from jealousy. (Mind you, that's nothing compared with what Tatsuya will do to anyone threatening Miyuki.)
This is amusing, I think. It's a big splash of transgressive subtext in a series that could otherwise have seemed dry. (This show isn't without humour, but basically it's a serious story.) Tatsuya and Miyuki are also a sweet couple. No, really. One almost regrets that it doesn't really go anywhere. The novels must surely have plans to address this eventually, but in the anime it's basically just playful inappropriateness. It's just a laugh.
Some fans object to Tatsuya and others to Miyuki. Which is fair enough.
I don't only like this show's characters, jokes and action scenes, though. It's interesting to think about. In addition to the worldbuilding and magical science, it has themes and political opinions. It's a right-wing show, although that doesn't mean what you think it means. "Left" and "right" in Japan don't have their British meanings, or even their American ones. Socialism doesn't exist there. Even the Japanese Communist party (which has a few parliamentary seats) isn't socialist, but instead talks about "democratic change within the current framework of capitalism" and "society above self". Instead, "right wing" in Japan tends to be bound up with nationalism and Japan's war record (including history revisionism).
Thus, in this series, Japan is the defender of righteousness, while the Great Asian Alliance is a sinister, machiavellian bully that regards state espionage as industrial policy and is willing to invade other countries. They're not called China, but you can find them in Chinatown and one of them's named after a character in The Romance of the Three Kingdoms. Yeah, it's China. (Also, this unflattering portrayal are a fair reflection of China's behaviour in real life and are even missing some obvious criticisms, e.g. supporting mass-murdering regimes in Syria, North Korea, etc.)
Paradoxically, this show is popular in the Chinese anime, comics and games community, albeit in a "so bad it's good" way, fuelled by the hype and controversy. They've nicknamed Tatsuya "Japanese DragonProudSky", for instance.
Apparently, the show's also negative about America and immigration, but I'm afraid I didn't notice. Maybe that's in the novels? Or maybe I'm just dim. However, I did notice all those samurai swords and armour at the end, not to mention the moment where a brief speech to a crowd inspires them to rise up to fight for their motherland. Oh, and the "not a nuke" magical attacks. Our heroes' hobbies include kendo and ninjutsu.
Then there's the first story arc having terrorists fighting for an end to discrimination, which the anime counters with a lengthy and detailed defence of inequality. In short, you can't legislate away the fact that some people are good at magic (for instance) and others aren't. Magicians have to work very hard and provide an invaluable service to society, while this group of terrorists is using fine ideals to cover up the fact that the specifics of what they're demanding are impractical, already implemented and/or just a self-serving handwave.
Again, I liked all that. It's giving the show personality. Regardless of whether you personally might prefer a less spiky message, you can't say this isn't distinctive. Besides, the show's arguing its points thoughtfully and is consistently taking a distinctive, principled intellectual position. Look at its discussion on whether to negotiate with the terrorists in ep.5, for instance. My main problem with the thematic content is that the intra-school bigotry and prejudice (which the show's attacking, by the way) is such a strong element in the first story arc that it's slightly jarring when it vanishes almost entirely from the rest of the show.
This is a thoughtful show with a strong storyline, awesome fight scenes and quite a lot of violence. It makes well-controlled use of its 26-episode run. Tatsuya is arguably the show's weak point, being ridiculously brilliant at everything and oddly uninvolved in the finale. By that point, he's a plot device rather than a character. The problematic content, though, I actively like, from the incest to the politics. It stops the show from getting bland. There's a lot of exploration of magical engineering and physics, but I liked that too. The characters are badass. Their enemies are willing to launch invasions. It's pretty cool, I think.