This will be your most harrowing shopping experience in Mexico unless you go to one of the few American-style butchers. Don't expect saran-wrapped sterility. Blood and guts are the usual scenario. When we lived in Playa del Carmen, the butcher killed a pig every other day or so and hung the bleeding carcass in front of his shop. Here in Cancun there is a municipal slaughterhouse. All meat is government inspected, but the butcher shops are still quite gruesome. Supermarkets are now the best place to buy meat, but don't expect American quality.
Mexican cuts are considerably different from American, both in flavor and shape. The local beef is astoundingly bad. The cows are a cross of Bengal tiger and goat so that they will survive in the tropics. They feed them fish meal and garbage and make them do aerobic exercises.
Ground beef is usually just dreadful -- old scraps of leftovers and dead fat. If you must have hamburgers, select the best cut of beef you can find and have the butcher grind it for you -- molido.
Pork, on the other hand, is usually excellent. The best cut is lomo de puerco, loin of pork, which you can have as chops -- chuletas -- or filleted in a single piece -- fileteado en trozo, saving the bones for making stock.
Don't accept a chicken from the counter but ask for one from the refrigerator -- el refrigerador. Veal is usually sold as milanesa.
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Zona de Tolerancia
Words to live by.