I liked it, although I understand its reception in general has been hot and cold. It's a fairly serious series, 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 wand. It's computer-assisted and you program it like software, although of course there's still old-fashioned magic that hasn't yet been computer-processed. Spells can be fired from guns. One of the protagonist's research projects involves the possibility of magically operated nuclear fusion reactors. Furthermore, we also have 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 they're invaluable for learning about the laws of physics for magic, 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, whereas I'd recommend watching them first. (The anime's based on a series of light novels, by the way, which often means 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. (Admittedly there are other "magic turned into science" anime out there, e.g. Chaika the Coffin Princess, but so far every one I've seen has been using the idea in detailed, specific and unique ways.) You get hackers, just as in real computers, and the reason for a hostile cross-border military operation is liable to be gaining access to a data warehouse.
There's plenty of other good stuff too. It's well paced, although I could imagine this making it look slow compared to overstuffed shows that are, say, trying to squash four novels into thirteen episodes.
The fight scenes are also superb. This isn't an action anime, but it's no holds barred when things do get ugly. Magicians are officially weaponised humans, so it's perfectly plausible for our heroes to be capable of taking down military targets, even though they're still at school. (Besides, a couple of them are also current or former soldiers and have live battlefield experience.) Thus there's nothing cooler than seeing a terrorist assault team attacking the school and discovering that they're fighting someone with ninja training, magic spells and the ability to pull your limbs off your torso. I don't normally care much about action scenes, but Madhouse are a top-notch studio and what we have here is very good indeed.
There's one legitimate charge one could lay, which is that our 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' magical attacks in real time and beat any opponent in combat. He scored 100% on the school's written entrance exam. His only flaw is that he failed the much more important practical exam, because he's bad at... um, something really important for magicians that in practice doesn't seem to slow him down much. Anyway, for most of the show, Tatsuya is outrageously brilliant at everything he does. Then, in the finale, we find out that he has additional secret powers that make him a combination of Jesus and Shiva, Destroyer of Worlds. So... yeah. It's actually quite hard to imagine story continuations that could actually challenge Super-Tatsuya, even though the original novels are still going.
Some fans can't take Tatsuya. I can understand that. Personally, though, I quite liked him. There's also more to the show than just Tatsuya and he's not overshadowing his friends. Besides, Tatsuya has other problems, e.g. he's being used as a minion by his scary family and he appears to have had almost all of 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 fairly common in anime and one might suggest that they're audience identification heroes for otaku with Asperger's syndrome.) Tatsuya is also obsessively fair-minded, will put himself to almost any amount of trouble if asked nicely and is strongly opposed to favouritism even when he'd be the beneficiary. We can forgive him being a bit cold-blooded.
The show's other potential problem is Tatsuya's little sister, Miyuki, who's an elegant lady of modesty, beautiful manners and a disturbing degree of brother-worship. The two of them are deeply inappropriate together. It flusters people. I bet it also flustered a lot of the Western fanbase, just like (in a different but equally transgressive way) Rentarou and Enju in Black Bullet. Fortunately nothing actually happens and at least Tatsuya's sister complex has its limits, so he thinks it's funny to make people wonder if he's incestuously close to Miyuki. He's teasing people. He thinks Miyuki's play-acting, just like him.
She's not. I think Miyuki's serious. She doesn't actually want to have sex with Tatsuya, or at least she's aware that doing so would be a bad thing, but it's very hard to believe that her feelings are just platonic. Threaten Tatsuya and Miyuki will freeze you into an icicle. She's even capable of covering everything in ice unintentionally, just because she's jealous. However that's nothing compared with what Tatsuya will do to anyone who threatens Miyuki.
This is amusing, I think. It's spurting a big splash of transgressive subtext into a series that could otherwise have seemed quite dry. (This show can be funny, but basically it's a serious story.) Tatsuya and Miyuki are also a sweet couple. No, really. The only thing I regret is 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 the show being playfully inappropriate. It's a laugh, but no more.
In other words, some fans have a problem with Tatsuya and others have a problem with Miyuki. Which is fair enough.
What I like about this show isn't just the characters, jokes and action scenes, though. It's interesting to think about. I've already mentioned the worldbuilding and magical science, but it also has themes and political opinions. This is a right-wing show, but you should be aware that that statement 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". Mind you, we could have a long discussion about their concept of "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. (Mind you, it has to be said that the fundamentals of 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.
At the end of the day, though, this is a thoughtful show with a strong storyline, awesome fight scenes and quite a lot of violence. It's nice to see such well-controlled use of a full 26-episode run. Tatsuya could perhaps be called the show's weak point, being ridiculously brilliant at everything and oddly uninvolved in the finale to boot. By that point, he's turned into a plot device rather than a character. However the problematic content 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.