First of all, I don't write reviews. I just watch the anime, take note of it, put a score on it, and remember it if was good. The fact that I'm writing this is quite important.
Now I gave this a 10.
Story: 10
I had just finished watching "The Mentalist", a television show about crime and mystery, with comedy in between. So landing on Kamisama no Memochou was great for me. I was able to enjoy the story because, like "The Mentalist" the story was well thought out. The story starts and follows the general mystery solving format that makes it good. First, recognition of the crime, planning, first scouting, planning, first action, and then the reveal. Or something like that. I really appreciate that the series takes ~40 minutes to start and end a mystery. This shows that Alice and the detective squad are really well at what they do. Now of course there were stories that took longer than 2 episodes. These stories...omg they were awesome. Each scene exists for a purpose in the development of the detective skills. Each scene progresses the MC and the viewer ahead and also allows us to find the personalities of the characters involved. For a story that is deep, proper, and meticulous in the way the mysteries are solved I really liked it.
Art: 9
I'm too picky about the art style since I understand each studio follows their own way of drawing. So every now and then I pause the episode to notice the detail in a frame. The art was well, nothing lazy. Sure, a few frames had simple drawing but nothing that would remove from the show a lot. Everything that needed focus had detail and that's all that mattered.
Sound: 8
Again, sound is great if it matters and if it doesn't then it's just another thing for the acoustic value in a scene. I like anime such as Kill La Kill and Katanagatari in the way they use a special song or tune for a certain type of situation or character (s/o to Blumenkranz for Ragyo). I noticed that in this anime there are a few empty scenes with no BGM. Otherwise there is something to fill the airwaves. And then there are a few reoccuring songs to match a situation, and I really liked that. I.e. when Alice explains something, a really cool female vocalization song starts in the background and adds a special intensity.
Character: 8
Never get your characters wrong. I really liked how the characters in each crime were explained in a nice and detailed way. Sure, some of them were regular characters that already existed in our knowledge before they make their "request" but still...characters that stay for a short time or have importance for a short time still get enough presentation to show themselves to the viewers. Characters with longer importance are slowly revealed to the viewers. And I liked that. The pacing of revealing the backstories of characters was great. There were a few episodes just to reveal the backstories of two characters, and another single episode to reveal the story of another. Each was very well presented. The NEETs are highlighted for their abilities, and they're "powers" are constant, no deus ex machina here. I really like the MC because he isn't the dense type and he is smart in his own way. His pairing with Alice is great too and in that way the viewers get the inside scoop on what she is thinking because, as they point out in the anime a lot, the MC is talker and not a thinker. The reason why I think the characters aren't super awesome is because, well the author uses concepts so out of the norm that it becomes unique...and that hurts it a little. Near the end I saw the MC become a little different and succumb to the generic MC style where "he is weak and confused but now he is strong, but isn't always strong...just when he wants to be" and that was annoying to me because I really hoped the anime wouldn't end like that.
Enjoyment: 10
Like I said, I just finished watching 7 season of "The Mentalist" in which I thoroughly enjoyed. Coming to this only helped extend the enjoyment I had in that show and so seeing the pacing of this anime and how there was a smart character who didn't do much, and a not as smart character who ran around a lot helped me relate back to "The Mentalist". For anyone who hasn't seen the show I'm talking about...well if you like to think a little in an anime and like a bit of problem solving and connecting the dots...I think you'll like this too.