Monk is one of my favorite shows. It's not gory or graphic. The actors are some of the best I've ever seen. The writing is extremely clever and witty. Other than a few innuendos or "sex-affiar," as Monk would call it, related crimes, there really is no strong sexual content. The main characters show each other respect and demonstrate what it is to be a true friend. Monk has a lot of issues to work through and each episode will likely have a moment in which you're laughing at some of his antics, or at some of the reactions to his antics, and then grabbing a hanky for a touching ending scene. I would recommend this show to anyone over 11. The only real issues are that some of the bodies, while tastefully filmed so that they're not graphic, may be just a little more bloody than you might want them to be. The murders can be very creepy so I advise parents not to let young children watch this. The language is very mild but it's nothing most tweens haven't heard from other TV shows they've likely seen.
I don't understand some of Monk's bad reception, personally. There are a LOT more violent crime shows out there and this one is full of heart, charm, and wit. It isn't about the murder mysteries. It's about a man who is trying to cope with his many psychological issues and it's about the people in his life who are willing to help him, no matter how difficult it gets. I think that's a very positive message.