Pretty funny to read this today as I am sitting in the Intercontinental in Polanco looking out over Chapultepec Park. This is my fourth time here in 1 1/2 years and I must say that it indeed is a very dangerous place. You have to consider the fact that you are always being watched and if you give the opportunity you will definitely have problems.
There is just an edge about this place that makes it uncomfortable for me and I grew up on the lower east side of NYC and can get by in Spanish to boot.
Of course as many people have mentioned if you stay local and don't go too much off of the beaten path you should be cool but I would be concerned about your nocturnal activities and being extra careful after partying.
Have a safe trip.