When I read previews of the Fall TV season, Terriers was one of the shows I thought had the most potential. I think Donal Logue has an easy charm to him, Shawn Ryan has showrunning pedigree, and I think Tim Minear has done great stuff on a wide variety of cancelled shows. But when I watched the pilot, I wasn't terribly impressed. It was interesting enough, to be sure, and it made me laugh, but it seemed like such a trifle.
I've continued watching, though at a fairly slow pace (just finished the tenth episode) and I don't believe that Terriers has gotten much better than that initial pilot. On the other hand, I have a much higher opinion of it. Yes, I know that seems counter-intuitive.
The thing that makes Terriers work is that it totally buys into its premise. In most TV shows, the characters have baggage, but it doesn't come into play often. So-and-so might be a recovering alcoholic, but it only comes into play in specific episodes when they're tempted into it. On Terriers, being a former alcoholic informs virtually everything that Donal Logue's character does. Same thing with his partner's dark past.
Because these characters are trying so hard, and because they're so well-defined and acted, this has the subtle but impressive effect of changing the overarching narrative of the show to one about characters instead of plot. While I think novelists have realized this for generations, TV shows (and most visual media, to be honest) have tended to rely on plot to drive their narratives. The Wire, for example, is such a success because while it is a plot-based show, it's the characters who drive the plot - everything stems from them and their understandable motivations. (Battlestar Galactica, on the other hand, collapsed in large part because it started letting the plot drive the characters, most notably the Final Five fiasco.)
What makes this interesting is that, in the aftermath of Terriers' cancellation, some of the statements by the FX network president indicate that audiences didn't find the show "edgy" enough, that it didn't fit the brand. The bitterly ironic part of that is that Terriers was edgy, in that I'm constantly emotionally on the edge of my seat (or the edge of a cliff) while watching it, because that's where the characters are. Its tranny hookers and cuckold-fetish husbands aren't particularly light fare either. You just have to do a couple episodes of digging to get to that point, and it seems that most people weren't willing.
This also seems especially non-revolutionary when you consider that it's generally how the best sitcoms work - they make you feel comfortable hanging out with the characters, and the characters' personalities, quirks and fears drive the storylines. Perhaps Terriers' foray into genre-bending helped lead to its demise. Still, I hope that its character-based long-term storytelling helps to influence television in the future - it's the best we can hope for after its cancellation.