The three Sinners of the System movies are a mixed bag. Being theoretically set a few months after the first Psycho-Pass movie, in practice only the third actually functions like a sequel.
The first is a side-story that completely overhauls Mika’s personality (for the better) and feels like it should be a prequel to the second season. It’s also not very good. The second is mostly a prequel flashback to the first season (framed by a few ‘modern day’ scenes set before the previous movie) focused on one of the S2 enforcers. This movie is quite good. And then there’s the 3rd movie, which…. Well, it’s sort of required watching if you plan to follow-up with Season 3, yet it comes across nothing like a Psycho-Pass work.
That third season begins after a multi-year timeskip, and quite a number of things have changed: Mika underwent another personality overhaul, Japan has relaxed its isolationist stance, Sibyl is gearing up to reveal its presence to the masses, Akane is off the team, and there are three new enforcers and two new inspectors. The old team is still around, just in a notably different role. It’s surprisingly good (clearly meant to be a return to Season 1 sensibilities) but suffers both from a number of unexplained developments and having Arata be so ludicrously overpowered. It also ends on a cliffhanger…
…resolved by a ‘movie’ follow-up. This bloated conclusion takes the concept of “homage” far too far. It apparently wanted to recapture the magic of the mid-series Season 1 climax, but instead stumbles time and again with both questionable action scenes and by just flat-out dragging things out for too long.
In the end it’s tough to recommend watching any of these besides the 2nd SS movie: The first is a pointless sidestory, the third lacks any Psycho-Pass sensibility, S3 requires having seen that third SS movie, and First Inspector is just plain tedious.