I realize one can get away with using dollars, just as until very recently as a U.S. citizen you didn't need a passport. It was the same for trips to Vancouver BC.
Maybe it's just me, but that always seemed vaguely disrespectful to me. If I'm visiting a foreign country, even a bordering one with whom we may have special arrangements, I'd rather do them the respect of using their country's currency, and using a real passport.
Travel tip: the Bank of America right by the Mexican border won't exchange dollars for pesos even for Bank of America customers, and the Wells Fargo right by the border has noticeably inferior rates (i.e. 602 pesos for 50 dollars instead of the 645 pesos which Melek, the most popular independent exchange service, offers).