For a show that was being hyped up by many to be like the 2nd coming of Christ for the mystery anime genre - it was a huge let down. Supposedly the light novels it's based on are amazing and are extremely popular in Japan, but this seemingly didn't translate well into anime format. I will grant it that if you alternatively watched it as strictly an action anime with a espionage myserty element it was fairly acceptable and could be subjectively described as decent or at least passable for the most part. But as a full blown mystery (which is what it's labeled and intended to be): the anime was a near colossal failure.
To explain what I mean by why it failed as a mystery anime, to put it most simply: it's because it didn't really leave a mystery for us to solve. Instead of having a plot or situation that made us think or rethink a situation, scenario or question - each episode pretty ends up just as a reminder that "oh, the Detective is eventually gonna die" (which is established at the end of episode 1 and the title itself) and how she dies is the so-called mystery of the show that we're waiting for. It killed any potential for tension or drama to build up and instead of climaxing on the top of a hill - the ending felt like we got finished getting off of a moving walkway.
The detective herself, Siesta, is also a point of contention within the anime. She manages to seemingly solve every problem by first glance and seemingly just let things play out as she intended to kinda tease the other characters. While it does make Siesta out to be this fantastic "Legendary" detective - it also made her an arguably Mary Sue type character. You either love her for it, or you hate her because she butchers the mystery aspect of the anime. I've seen both opinions and land somewhere in the middle personally. How much you enjoy the anime likely comes down to where you fall within this scale since she is the focal point of the anime.
The animation quality was a topic of controversy throughout the show's runtime. While the first episode as well the following few were made very well, the middle to end of the anime was definitely made with less notable effort. Artistic features didn't line up, characters were not consistent from shot to shot - even missing important details like types of clothes they were wearing in one episode even. I found out later that these episodes were outsourced to save on budget, and it shows unfortunately.
The fight scenes, especially at the beginning of the show's run, were intense and well done. But the later fights were either really dumb or poorly executed. We go from stopping a terrorist planning to blow up a plane to... chasing around a drug dealer in a easter bunny costume at a middle school culture festival. The last fight with the Chameleon in particular was not good and me sigh and shake my head with how far the quality fell off from what we got at the beginning.
The characters, while mostly 1 dimensional, were interesting and enjoyable. The MC was also a not-so-dense dry humor type of guy; which made him so much better than a lot of generic dense and stupid ones out there. He evolved throughout the show and was probably the reason I kept watching after they killed off/sidelined the detective herself. The others members of the main cast were alright, but not overly spectacular. The villains were dreadfully awful though, vanilla bad guys with mutant superpowers and the usual generic "take over the world" plan. Hel was the only exception and they sadly gave her hardly any attention.
The one thing of note that I will credit this anime with is that it was faster paced than some of the other mystery genre animes out there, which has been a historically reccuring issue that has plagued them as a common complaint by many people. For example, I remember watching In/Spectre (another supernatural mystery anime) a few years ago being incredibly slow and was hard to watch because it didn't make much progress and the action was very sparce. Detective definitely did a better job of not boring the audience through long dialogues and breakdown of each scene, instead opting for more action and briefer breakdowns of the crimes in question. While it made it less successful as a mystery, it made it more enjoyable (or at least bearable) to view as an action anime. This is probably the biggest reason why folks like myself who despite watching the quality fall off at least managed to continue on and at least finish it.
Music was okay. The OP was fairly good. while the ED was plain, generic and nothing special. The background music used throughout the anime felt fitting, so no complaints there. Wasn't out of the ordinary, not bad but not special. Pretty par for the course (which is sadly this anime's best quality).
It's a shame that this show ended up as the dumpster fire that it is, because I heard from light novel readers that there was so much they didn't put in that could've made this a genunine and propper mystery thriller. With the right execution this very well could've been the "second coming of Christ" equivalent for the mystery anime genre. But now it it serves as a lesson of why animation budget management is important and what you need to do to avoid butchering a mystery plot.
You're better off going into and trying to enjoy this show as an supernatural crime fighting action anime rather than a mystery - because on that front it's kinda enjoyable. But if you are looking for a true mystery anime, I'd keep looking. Because as a mystery: it is a massive failure. For something that was supposed to put mystery animes back on the map, The Detective is Already Dead managed to do the opposite and sink the genre's marred reputation in recent years lower into the ground.
In conclusion: I wouldn't reccomend watching this to anyone unless you're genuninely interested in reviewing it for the sake of analyzing it's failures for research purposes and comparisons, especially amongst the many mystery anime flops in particular in the past couple of years - there is a lot that can be learned from this mess. But you're likely not gonna have a fun time as a casual watcher with this one. Unless, you're like a Date a Live fanboy who'd get really stoked about the main girl being a near identical twin of Origami Tobiichi (seriously, a suprisingly large portion of the DAL fanbase was weirdly invested in this series when it was airing for that factor alone) in which case, you do what you wanna do with your time.