You don't want to mash the berries or bruise the tomatoes. Not all farmers' markets have bathrooms, unless you count portables. Go before you leave home. Crowds, close quarters and unevenly paved open lots at farmers' markets can make baby strollers impractical. If you're going to an unfamiliar place, call ahead to ask about conditions.
Strollers are usually less of a problem at the smaller, less crowded on-farm markets.
Try not to buy too much, although it's hard to say no to great food at good prices. If you can't resist, share with a friend or neighbor when you get home. Better yet, bring someone along.