First, the positives. Visually, Production I.G. does a great job in all areas. The animation is nice and smooth, the world design rich, the character designs memorable without being too flamboyant. The more elaborate setpieces also showcase some pretty nice cinematography.
Sound-wise I'm also a fan, not just because I love Rin Toshite Shigure, the background music is also pretty decent and the voice performances are good. As a long-time fan of HanaKana I especially enjoyed seeing her in a more serious role, and she delivers competently as Akane Tsunemori. The rest of the cast is quite star-studded, and none of them disappoint.
The characters are for the most part well-written as well. The cast size seems just right, and the show does a good job of focusing mostly on developing the central characters and giving them engaging arcs without sacrificing pace or world building. The significant exception is the main antagonist, who I will get back to.
Now, for the main part of my review and where the problems lie: the writing. This will be difficult to go into detail on without spoilers, so be warned. First of all, let me say that I consider Urobuchi Gen to be a very competent writer, and loved his work on Madoka and Fate/Zero, which just makes his failings here so much more frustrating.
First, the setting. The dystopian sci-fi is one of my favorite genres, as it's a great medium for looking at contemporary social issues in a more removed way making it easier to recognize (in Psycho-Pass, for example, the idea of digital surveillance is taken to extreme lengths), as well as a tool for examining current technological progress and the potential implications of it. While Psycho-Pass' setting is not the most unique one (the "stopping crime before it occurs" bit is probably most famously explored in Minority Report), it seems like one that should be ideal for exploring a wide range of interesting questions around technology, ethics, crime, surveillance, mental health and a wealth of other areas.
However, for the most part the show just ignores that it's set in an oppressive police state dystopia, and is more concerned with run-of-the-mill cop and robber stories that just happen to involve the sci-fi technology. There is some hinting at government corruption, and at times it looks like Tsunemori is going to bring down the insane brain scanning system and change the world, but ultimately the only thing she does is give the system an upgrade and continue being a cog in it. Unlike the finale of 1984 (one of the many classic dystopian sci-fi works namedropped during the show), where the surrender to to Big Brother reads as a tragedy, as the protagonist being crushed by the oppressive system, Psycho-Pass' protagonist only ever takes issue with specific details of how the system operates and even when confronted with real criticism flat-out ignores it and continues happily maintaining the system.
But hey, at least the criticism is present, right? Well, kind of, but not in a way that supports a reading that the protagonist is not the moral center of the story. As an example, when Tsunemori has a problem with the indiscriminate murder of would-be criminals as defined by the Sibyl system, her solution is to set her own gun to stun mode. This tells us a lot about the views of the person who wrote it: The moral thing to do in a situation like this is to take the most ethical action you can while never breaking any rules or challenging existing power structures in any way.
To be fair, there is one source of actual scathing criticism of the system itself: Makishima Shougo, the main antagonist. However, the way this character is presented is probably the most damning aspect of the entire show. Before we're even properly introduced to his ideology, he's shown as a cackling psychopath who happily kills random people just to prove that he's able to. Contrasted to Tsunemori's calm, composed and by-the-books demeanor, it's made ridiculously explicit that this is an insane villain whose ideas are not worth entertaining.
Overall, the moral lesson of Psycho-Pass seems to be that radical change is never an option, and the only way to improve the world is by working within the system and never breaking any rules, no matter how oppressive the system becomes and how little room you have to maneuver. Also, anyone who threatens the current order needs to be destroyed, preferably with a bullet which makes your entire body blow up in an almost comically gory fashion. What implications this ideology has for contemporary politics should be obvious.
Finally, it's hard to look at Psycho-Pass and not compare it to Ghost in the Shell, another Production I.G. franchise. Both are dystopian sci-fi settings featuring a female cop who leads an elite squad of special enforcers (and both love quoting/namedropping texts it's supposedly inspired by). However, GitS, in every iteration of the franchise, has always shown a willingness to explore the interesting ethical questions surrounding the technology and world it presents. Psycho-Pass' unwillingness to do the same does not make it look good in comparison.
