Concrete Revolutio is a very different show than what we get usually. It's a show made by <a href=http://anilist.co/staff/101490/ShouAikawa>Shou Aikawa (most known for the infamous <a href=http://anilist.co/anime/121/HaganenoRenkinjutsushi>2003 Fullmetal Alchemist adaptation), but has plenty of episodes actually written by other writers (such as <a href=http://anilist.co/staff/105308/GenUrobuchi>Urobochi and <a href=http://anilist.co/staff/98328/KazukiNakashima>Nakashima). It is set in the '60s, and deals with the post-war period of Japan through a very Watchmen-like lens. Not happy with just that, it's also achronological, going through characters past, future and present all at the same time.
Because of these things, Concrete Revolutio is a very uneven work. The world it builds is mostly consistent in itself - though one can expect almost everything when your premise is "supernatural entities are real and kind of everywhere" - but the characters can be all over the place depending on the episode's themes, writers, and chronological setting. This can be rather jarring for people.
However, it works really well for the kind of story Concrete Revolutio is telling. It's not a story about the characters it built. It pretends to be one, but it's very clear - from the way the dialogue is written to the conclusions the characters come to - that this is a Message Anime. This story has A Point. And it damn well will make you listen to it.
It takes the "seigi no mikata" Japanese spirit (often translated as 'superhero', 'hero of justice', or alike) and puts its own spin on it. When the supernatural is abundant, what's a real superhero? The guy who protects the world from giant kaiju-like (think Godzilla) monsters seems like he's a pretty safe bet, but what if he's actually half-fused with a criminal alien? Can a super robot fully understand justice? Is it wrong to just want your kind to be safe? Is it wrong for me to want to protect Earth-chan?
You might've noticed those are actually kind of complicated matters, though the central point seems so simple. It doesn't help that Concrete Revolutio has so many viewpoints on all kinds of issues: it's not here to give you a clear answer. Though its message is loud and clear, by way of main character Hitoyoshi Jiro, its themes, explored by the plethora of different characters and messages they bring, are all complicated in their own way. Unfortunately, the show only has 24 episodes to elaborate on those, so several feel underused and underexplored at the end. But that's still mostly okay, because Concrete Revolutio is almost episodic in nature. And most episodes deliver their points.
In fact, given this character-writing and episodic nature, it's actually too dense to fully explore in one review. One could spend paragraphs talking about Earth-chan's simplistic views of good and bad, and how that gets challenged by her own nature, a contrast of Hoshino's. Shiba's character development, the way his humanity conflicts with his programming, and how he mirrors and contrasts Jiro. The Superhuman Bureau's tough compromises and schemes in order to accomplish its one goal: peace. There's just too much. What I can say for certain about this series, whether one will like it or not, is that it has fuel for a lot of discussion. In fact, one common complaint (?) one can find is that this show is more interesting to talk about than to actually watch.
Which comes to the talk about execution. As said before, character-writing and especially dialogue that incurs from it is very "making a point"-like, often not feeling like an actual conversation human-beings (or not) would have. The achronologicality of it all, in-episode and between episodes might throw you off significantly, and charts to get a hold of what's supposed to have already happened at which episode do exist, and might even be necessary for some people. Several anime or Japanese culture in general references might fly by your head if you're not an afficcionado or actually looking for a list of references. It's a difficult show to follow fully.
On the less story-telling/meta aspect of the series, the art style and animation are interesting, to say the least. The pink, flamboyant, cartoony tone everything has might remind you of the '60s look and invite you in, or look garish and make your eyes hurt. As characters are often references to other works, the character designs are anything but consistent. The animation varies wildly - while Concrete Revolution managed to have some gorgeous bits here and there even while studio BONES was in charge of three shows during its second cour, it's mostly average/passable at other points. The sound design is better exemplified by the first ED, below. Often having psychedelic tunes, mixed with rock and some general pop, the soundtrack fits the time period and never once takes you out of the experience - often times enhancing it.
One needs to approach this show with a very open mind. It is a very flawed work - mostly on its story-telling front, though also in other areas. However, I myself found the issues passable in order to enjoy the thought-provoking ideas, the incredibly dense discussion it can provide, and even the intricate references and timeline. Hopefully this homework of a show can find a place in your head, too.