I've only seen a few episodes, but my main quibble about this series is that sometimes the teaser either reveals whodunit, or it's otherwise fairly easy to figure out whodunit (the how and why, of course, is a different story). Aside from that, the show has a lot of positive things going for it: it has some funny moments (one episode had me laughing so hard at one point that I didn't even hear what the characters were saying), the main cast is effective and make the characters likeable, and there's a different case every week (no complex conspiracies or spy stories threaded through the whole season), and there's a great protagonist and sidekick: all the elements of a traditional detective show. It's an obvious tribute to classic detective drama and the cinematography even has an '80s-'90s style to it (hard to describe, but if you see it you'll know what I mean). Really, the only other negative thing I'd mention would be hearing too many Canadian accents from actors who are supposed to play characters in San Francisco (from which I guessed correctly that the show is filmed in Canada). And this isn't about the show itself, but I wish ABC would air the episodes in order! It's been all over the map, which is not a great way to introduce folks to the show. How confusing...
I think of Monk as a loose, contemporary setting of the Poirot series, with some character tweaks. Adrian Monk (Tony Shalhoub) is a version of Poirot: formerly on the police force but now an independent investigator, and he puts Poirot's obsession with order and neatness to shame with his own sudden obsessive compusive disorder. Except Monk has just lost his wife, and is still dealing with life without her. Then there's his sidekick, diligent Sharona, Adrian's nurse/assistant (Bitty Schramm) who's generally no-nonsense, but sympathetic and understanding when she has to be (select aspects of Miss Lemon and Hastings in one character?). I love one scene where Sharona's son is with her on a pseudo-stakeout: he says something about Monk looking for something; she tells him to do his homework; he responds with "You have a weird job." :-) And of course there's Captain Stottlemeyer (Ted Levine) of the SFPD (complete with an Inspector Japp mustache), who still asks for Monk's help on cases. Another cool thing about the show: good music. It's not the same style as Christopher Gunning, but Jeff Beal features some cool Django Reinhardt-esque guitar work in his score (much of his work on the show is available for download in MP3 format). [Official Monk Site]