It's a noitaminA show which I very much enjoyed. There are many people that disliked it, but I was not one of them.
Subete ga F ni Naru is a mystery detective show, and, unlike Ranpo Kitan (previously shown on noitaminA), actually has a mystery and detective work. It's a closed room story -- and I found quite interesting. Granted, I don't watch or read many detective stories, but this one really captivated me.
It is similarly driven by deeper themes -- philosophical questions about the nature of a person, freedom, love, death. Some found it shallow, pretentious even -- I didn't. I felt like the questions were asked naturally, answers proposed cautiously and not simply, as a lesson from a mentor. There are many doubling themes over the series.
The Perfect Insider has two timelines, one, with Saikawa and Moe, and the other in the past, with the young Magata. Both of them are engaging an important to the plot, if a little slow in pacing. I enjoyed the slow build-up, as I absolutely loved the characters interacting. I watched the whole anime in two sittings, introductory 2 episodes, and then 5 and 4. I recommend that you marathon it.
The three most important characters are considered to be very bright (Magata a genius, even), and seeing them interact, their wordplay, the dense relationship they have, the three of them, was very compelling. I found it very well written in this aspect. There are also secondary characters like the Director Shindo, or even less interesting ones, which are very one dimensional, but the main characters are fleshed out quite deeply.
Visually the series was stunning. The simplistic yet extraordinary character design, the animation and emotion that it conveyed, the backgrounds, the dawn scene -- all were remarkable.
As for the sound: voice acting was generally great, apart from the infamous long English scene that felt somewhat forced vocally -- as it made perfect sense from the plot point. OP/ED are remarkably good, not obvious both in their tune as well as visually. The OST had some remarkable tracks.
The Perfect Insider is not a perfect anime, however. There are some inconsistencies, or the animation suggests them -- the placement of the second body. The importance of virtual reality in the story even though the viewers are only introduced to it in 6-7th episode. The field of Saikawa and Moe is not clear -- just that they are extremely brilliant, and that Moe is good in maths. And yet she disregarded an important clue. But this can be explained that a) she's not a programmer or a mathematician per se b) she's a person and makes judgement mistakes. There is also an issue with Shiki Magata's sister -- Maki, and her recognition by the directors wife. Again, perhaps rewatching the series would clear those questions. I am certainly going to do so.
Unfortunately, despite being an opening novel in the series, the anime will probably not get a next season.