This is going to be a strange review because I have plenty of good things to say about the show but unfortunately find myself giving it a thumbs down.
Take away the "Watchmen" elements and the show is pretty damn good. It being set in the Watchmen universe adds absolutely nothing to the plot whatsoever. I'll give them credit that the Watchmen easter eggs are well thought out, but are completely unnecessary for the purpose of the plot.
Setting it in the world of Watchmen creates the expectation that, well, it will be about the Watchmen. And I'm not one of the fans who believes the Watchmen universe cannot ever be explored or adapted. I'd point to the most recent example to use the universe, the Doomsday Clock comics. That story manages to use the existing characters while introducing and expanding on the overall Watchmen universe.
This show does not. It should have just been set in an original alt-history universe instead. It honestly feels like it was originally because the first 10 to 15 minutes really set up the major differences in this timeline compared to ours, with the changes to the way police operate, the changes to the law and the changes to the culture. The first three scenes give you everything you need to know, and absolutely none of it is reliant on the Watchmen universe.
When I see a show set in the Watchmen universe that is aptly titled Watchmen, I'm going to be disappointed that I don't get that end result, even if the show is technically good. To make an extreme comparison, it's like how the Room is inadvertently a hilarious comedy, but if you were watching it based on it being a serious drama like it was advertised as, you'd ultimately be disappointed and acknowledge that, even if you are able to get entertainment from it, it failed at being what it set out to do.
So, the long rambling TL:DR is, as a Watchmen adaptation, the show falls very flat, but take it all away and you actually end up with a pretty good show with a very strong cast and the potential to tell a really good story.