When I first heard about Gotham Central, it seemed like a sort of "dream team" book for me, almost as if I'd been given the choice of who to place on the creative team. With Ed Brubaker and Greg Rucka as co-writers and the talented Michael Lark covering the pencils, it was three of my favorite creators all in one place.
Of course, if they were doing some random DC hero I'd never heard of, I don't know if that would be enough to keep me reading. I'm not a big reader of super hero comics in general, and my understanding of DC comics in particular is filtered heavily through the WB animated Batman, Superman, and Justice League series. As a consequence, I was really pleased to see that Gotham Central was slated to be a police procedural set in, well, Gotham. I'm a big fan of the larger comics companies spreading into a broader range of mainstream genres, and even a title that is nominally set in the DC universe has a lot of room to have its own identity.
Gotham Central tells the story of Gotham's Major Crimes Unit, a sort of "homicide, kidnapping, and other bad stuff" unit that is distinct in Gotham's police force by dint of being largely noncorrupt (this is one of the major problem areas you already hit in portraying police in Gotham -- in some Batman titles, they are nearly universally corrupt, and in other conceptions, they are entirely ethical -- I think GC hits a nice middle ground here). Their stories do dip heavily into the realm of supervillains and how a police force interacts with a super-vigilante on their turf, so it's not strict police procedural by any means, but at the same time, the series has a nice, real-world verisimilitude going on, and I end up buying into the protagonists' responses to what's going on around them. The characterization and storytelling are both quite strong, which is what I've come to expect from both Brubaker and Rucka.
At the same time, GC suffers from being placed in Batman's world. In particular, the series faces the same problem that Batman and other super-titles face in general -- the good guys are forced to be truly stupid from time to time. This isn't Dark Knight where supervillains and novel and no one's dealt with the Joker before. When a cop in GC decides to roll up his sleeves and "teach the Joker a lesson" I instantly checked out of the story. Of course the Joker is going to overpower him. Of course the Joker is going to grab the cop's gun and kill a lot of people. It's the unwelcome heroic parallel to easily-escaped supervillain death traps. The other major related issue is being stuck with "big events." Stupid Gotham earthquake storyline? Check. Stupid "final night" storyline? Check. And so forth. I just try to read around these things (and for the most part, that works well enough).
On the whole, I recommend the five available Gotham Central volumes. They are: