Fresh Meat

Most meat in the US and Canada has color added to give that nice red look. In Mexico this is not a common practice. Dead flesh turns grayish, so don't be put off it unless that gray has a greenish or bluish tinge, or smells "off".
Cook fresh meat the day you buy it.
Mexicans have a much more liberal "palette" compared to the sanitized tastes of her northern neighbors. You will find many more animal parts for sale, and many different types of cuts. They also eat a wider range of animals than we do. Experiment, but do so with guidance.
If you request your meals be served hot you probably won't experience any unnecessary problems.
Chicken should be treated like it is radioactive, until cooked (just as true in the U.S.).
Wash your hands after handling untreated, raw food, and frequently when preparing food.
Pork and bacon are excellent.
Bring your own deli meats such as salami, hot dogs, sausage, etc.
Mexican butcher shops are called Carnicerías in Spanish. Steaks are called Bistec.
Eggs are excellent.
Milk is inexpensive.
Chicken is of excellent quality.

Vegetables and Fruits

Mexico has a wonderful array of fresh fruits and vegetables, and if you are going to be in the country for any length of time, you will want to shop at the "mercados" (market) and peel the fruits or boil vegetables. Fruits and vegetables should be washed in sterilized water so that a weak chlorine bleach solution kills offensive bacteria.

Cleaning and Eating Vegetables and Fruit

Always wash, then soak in water containing 8 drops of iodine solution or 1 capful of bleach, for 30 minutes.
If you peel it before eating, you are safe.
If you cook it before eating you are safe.
If you want to eat it fresh, choose only unblemished items, and ALWAYS go through the wash/soak process.
Avoid fresh salads (they may not have been washed in bottled water).
You can find a much variety in a Frutería (Fruit shop) than at the supermarket and prices are cheaper.

Shellfish and Hot Weather

Shellfish tend to spoil quickly. This is especially true when the weather is hot. Even though you love your oysters, the possible results are not worth it.

Fish Stores sell fillets of fish rather than the whole fish.
Canned tuna is available everywhere.

If You Do Get Sick

Even if all of your careful precautions should fail, and you get sick anyway, you know that you are not helpless. Many well-meaning articles have suggested "toughing-it-out" with intestinal ailments, and "letting nature take her course". Checked with your doctor before you leave home, and obtaine a prescription for "Bacrtrim F" tablets (also available in Mexico without a prescription). Bactrim effectively annihilates offensive bacteria within twelve hours after dosing. To control watery stool, you can also take Lomotil. Occasionally an unfortunate forager will come into contact with food poisoning. The symptoms are usually quite pronounced and "miserable". Happily, the most common variety of food poisoning in Mexico (infrequently encountered however) lasts only 12 hours. The only cure for food poisoning is time. Sipping sugary soft drinks is a good way to maintain energy. Make sure that you drink enough while sick so you avoid dehydration. Drinking Gastrolite (a powder you add to water) or even Gatorade will you stay hydrated.