The story of Mouryou no Hako (or "Box of evil spirits" in loose translation) is a dark mystery taking place in postwar Japan that follows a group of investigators solving a case concerning bizarre murders of schoolgirls, whose bodies were dismembered and stuffed into boxes. The distinctive features of this story are supernatural Shinto elements and complex non-chronological storytelling with numerous surreal, mind-bending scenes. The latter, apparently, was supposed to make the series more thought-provoking, and it did make my brain work quite a lot... until I realized it's all done for a fundamentally wrong purpose. Unlike in Paranoia Agent or Boogiepop Phantom where the puzzle is put together step by step and the non-chronological storytelling is employed to make this process more interesting, here it's used to make the series as baffling as possible until one of the characters simply explains everything. Moreover, we don't see how he looks for evidence and comes to his conclusions - they're presented as facts, as if he knew everything beforehand.
Besides, the anime spends two entire episodes showing the characters sitting round the table as they drink tea and discuss the Mouryou phenomenon, using myriad of facts from Shinto and folklore. While I love everything supernatural and thought-provoking, that explanation turns out way too long and complicated: the main idea is pretty clear but the details are very confusing and have little to do with the actual investigation. And exactly like with the previous aspect, the show could have revealed the nature of Mouryou gradually in the course of the story by making the characters investigate it, instead of subjecting the viewer and the characters to being lectured in an almost indecipherable manner by a certain guy who just happens to know everything beforehand.
Speaking of the positives, however, I like that the show takes place in a realistically portrayed historical setting and that it's performed in classic noir style, rare for anime. Also, I really enjoy how dark and mature the story is as it touches upon very serious topics, and eventually the whole "Box of evil spirits" phenomenon turns out to be a powerful and surreal allegory of how the evil emerges and grows in a lonely and suffering heart. In other words, I like the show's themes, setting & dark mood, but not the actual way of storytelling it employs.
ANIMATION & SOUND
If you've watched Aoi Bungaku Series, you know what to expect from this anime as it comes from the same people who did the Run, Melos! chapter of Aoi Bungaku, and thus they are similar in style & quality. If you haven't, I'll just say that the series features: excellent visuals, full of awesome cinematics and mind-bending surrealism; attractive yet realistic character designs by CLAMP; very good soundtrack, both BGM and songs; and impressive voice-acting. In other words, what we have here is another example of quality by studio Madhouse, and the high production values are certainly among the strongest aspects of this series.
The show boasts a potentially brilliant cast that consists mainly of adult & clever men: a detective, a writer, a psychic, a reporter and some others. Also, it comprises a beautiful movie actress and those schoolgirls with a yuri relationship between them. However, the anime is too story-driven for its own good: until the end it spends most of the time on discussions and playing with chronology, using the characters predominantly as mere pawns & mouthpieces. At the end it finally introduces some character development and serious drama, yet it appears insufficient to make the cast memorable and get you attached to any of them. Besides, as I have already mentioned in the story section, the show exposes crucial information and resolves the mystery with a help of one character who simply knows everything instead of making the characters come to those conclusions using their logic; which means most characters don't fully display their abilities in the course of investigation, and that disappoints me quite a bit. So, my opinion on the cast is the same as on the story: I like the characters but not the way the series handles them.
While some viewers consider this anime an underrated intellectual masterpiece, I think it overcomplicates itself for the wrong reason; explains the mystery instead of solving it; and never does its characters justice because of that. However, it does have a number of strengths as well, and in general I enjoyed the series even though it could be better than it eventually turned out to be. So, it might be worth giving a try as long as you don't expect a masterpiece, and you are ok with the slow pace and plenty of expository monologue it has.