I've been here a couple years now. Regarding the violence, it's mainly in the northern border towns, and a few other concentrated areas. I live in the capital, and it's really not a problem at all here. Frankly, I live in a yuppie neighborhood, drive around in my own car, hang out at nice clubs and apartments of fairly well-off friends, and after two years here, have not had the slightest interaction with any violence.
There are third big impressions I've had here. The first is that girls (and people in general) aren't comfortable saying "no". If you meet a girl and ask her out, even if she says she wants to go out, it's completely up in the air whether that will ever happen. So many other foreign guys agree: girls here are always cancelling. Or, they'll ignore a phone call, etc., only to call you out of the blue 3 weeks later wanting to hang out then. Very unpredictable. Same with business meetings too ... a big frustration for foreign businessmen here is how often they've been blown off for meetings, or people showing up really late.
Secondly, in business, friendships, and meeting people while out on the weekends ... people are just much more "closed off" than Americans. It's much more of a society where people just stick to the people they know. Compared to America, where people move around a lot, move to a different city for college, then a different city after that for their first job, etc., people here are much more likely to have lived in the same city for their entire life. Compared to a girl at an average twentysomething/thirtysomething bar in the States, a girl here is much less willing to talk to a guy she doesn't know.
Finally, there is so much more income inequality here, and that really affects the interaction. At least for me, the people I interact with through my job and some classes I've taken, nearly all of them have maids living in their house, some have personal drivers, etc. Ha, I remember the time I had to go to an event, and a companion told me he would pick me up. It turns out that meant he sent his personal driver to pick me up. None of this I saw growing up in a pretty well-off suburb. People joke about foreign women looking for a green card, but with the Mexicans I spend most of my time with, they have no interest in that at all. And because these people have lived such coddled lives their entire life, they are even more closed off to talking with new people. Being an American here isn't impressive at all (European, French in particular, is a whole other story).
All in all, I'm reasonably happy here, though I'm leaving fairly soon. I have a solid group of friends, enjoy what mostly fellow expats (not purely by choice, but an expat is much more interested in making new friends than a typical Mexican). This whole experience has really made me appreciate America's openness.
Just my two cents. Cheers!