story: most of it straight from the manga, no details left out!
honestly, the show was just spectacular. I tend to read the manga's first before viewing the anime, and most of the time a lot of details were left out, but with this everything was roped together pretty perfectly! They showed each short story in order(save from the first one) and they animated it pretty creatively too!
Although I am a bit disappointed that the first story wasn't there, I can't complain because everything else was just amazing.
animation: they kept it in the author's original style!
the animation was very clean, and it had that 'mystery' feel to it! I've always liked the older art styles of anime since I basically grew up with it, and most scenes had that sort of 'drained' colour pallet which really helped emphasize the ominous and creepy atmosphere of the stories.
sound: pretty good for a 90's anime, not too shabby but not amazing either
for the english dub, Count D's va was a nice choice, he kept the mysterious feeling and really tried to get into character, although Detective Orcott's Va was err interesting to say in the least.
characters: the characters were represented pretty well
the characters in this show are phemonal! although its kind of saddening that they chose the more plain characters to animate. my personal favourite in the manga was Pi-Chan, so I guess you could say I'm a bit biased when it comes to this part www
I like how they didn't try and overexaggerate some of the characters like some other shows, and how they stuck straight to the book!
misc: i really wish that the other parts of this story will be animated
(although it likely won't), because the first few stories in the PSOH stories focus on the creatures, while the others focus more on the characters and backstory, and then it goes into the lore of things!