If you need to make any phone calls while in Mexico buy an international phone card (like a Latadel card) at any market and use that from your hotel or pay phone. The phone system in Mexico is unregulated and if you use your home calling card (ie Sprint, AT&T, etc) you might end up with a surprisingly hefty phone bill. Making calls from pay phones without a Mexican phone card can cost up to $40 US just to CONNECT the call. It's a totally unregulated system. So beware. If you need to make a call from your hotel room make sure you talk rates with the front desk first. Also make sure you buy the phone card once you're in Mexico. My friend bought one in the States and was unable to use it down there.
I've never had a problem with this but I know others that have, mugging and things coming up missing in your room has been reported more than once. And all to many have returned home with the (pardon the phase) "runs" after spending a little time in Mexico ... so drink something from a bottle, beer is good! But if you must have bottled water drink that. Most nicer hotel have water filter systems for the in room water supply.
I know this goes without saying, but watch your bags. Especially in a crowded city like this. A friend of mine travelling in the group with us had some things stolen out of his backpack that he had under his arm on the subway. They slashed his bag with a razor (we assume since it was a clean tear) and we didn't even notice until much later.