I didn't think much of its first couple of episodes. They were okay. The show seemed fairly unremarkable and on another occasion I might easily have dropped it. It's a magical girl show with an embarrassed heroine (Matoi), a super-enthusiastic best friend (Yuma) and a mentor with big boobs. These are familiar elements.
However I kept going and found myself liking it more and more. It stops being about magical demon battles. There's character development as Matoi helps Clarus thaw into a human being. Matoi's family turns out to be the heart of the show, with her long-gone mother (Shiori) and her workaholic father (Shingo). This creates mother-daughter resonance and themes of protectiveness, trust and honesty vs. secrecy.
At first glance, it's a common anime set-up. Matoi (13-year-old schoolgirl) and Shingo (policeman) live at a shrine that's run by Yuma's embarrassing father. He's a lecherous priest with goofy hair. Everything seems normal, to the point that the show doesn't yet have that much personality. The girls are nice. It's fine, but nothing special. One day, though, Matoi learns that she's a magical girl who must fight monsters! (Well, "exorcist girl". Different name, same thing.) She defeats a demon, then discovers that her clothes don't return when she turns back into her non-magical form, because nudity is funny.
That's about the extent of ep.1, if you ignore the other boob jokes. Let's do that.
Things develop, though, and the show gets less generic. The Vatican has an exorcist division called the Anti-Creed of Fatima, with a soldier (Clarus Tonitrus) who hasn't been able to smile since SPOILER happened years ago. She's a magical girl like Matoi, but she needed training and mechanical assistance. Deep down, she's limited, unlike Matoi who gets her powers from a god and yet never even wanted them in the first place. She wants to be normal. Dream on, girl. That's not going to happen, especially when magical girl footage gets uploaded to the internet and has 50 million views.
Yuma, in contrast, loves exorcist girls. She can't understand why Matoi (doesn't want the job) got chosen instead of her (manic shrine maiden who dreams of fighting monsters and isn't beyond breaking the fourth wall). She'll make an internet website where people can click for requests. Yuma's great.
There's a motif of "trust me" and "believe in me", invoked by both Matoi and Shingo even though Matoi's not telling her father anything. He can't recognise her Exorcist Girl form, perhaps because it seems several years older than her real one. Should she tell him? If she doesn't, he'll just order her not to visit dangerous places... and she'll even obey him! (This is capable of endangering her friends.) This is then taken to the next level in the last few episodes when we learn that no one ever told Matoi or Shingo the truth about Shiori.
There's a supervillain with a nasty schtick. He'll body-jump, but his victims don't get their life energy back afterwards. However he turns out to be oddly irrelevant and it's almost a surprise when he wanders back into the story near the end for a sort of cameo.
It's nice. I liked it. Nothing here will change the world, but it's entertaining and I liked the characters. It can be lovely and funny, e.g. ep.6. It had the potential for some interesting juxtapositions of monotheistic Christian vs. polytheistic Shinto conceptions of deities, with agents of both religions participating in the fight against extra-dimensional demons. The show doesn't go there, but theoretically the contrast's in there. (Oh, and that's all in what seems to be a 24-dimensional hard SF universe.) To my surprise, I'd recommend it.