I breastfed three babies, and never once had to “whip my boob out” or had a boob “flop out” or any such catastrophe—even when sitting on my living room couch with no one around except the baby. Or toddler, sorry @AstroChuck! For a woman to “expose herself” while breastfeeding in public, she’d have to be trying to get that boob out there for the world to see. It’s very easy to get the baby latched on without exposing anything, and takes very little practice to do correctly. Once the baby is nursing, his or her head blocks any kind of view.
Once, my husband’s best friend unexpectedly stopped by our house and walked into the living room while I was nursing a baby. My husband tried to steer his friend over to a seat on the couch, but the friend first walked over to see the baby. He said, “Oh, he’s sleeping!” then walked across the room. He had no idea I was breastfeeding, and didn’t pick up on it until my husband and I couldn’t stop laughing. Then, he was embarrased.
I think most men would rather avoid scoping a peek at a nursing mom’s boobs. Aren’t they more likely to look away as soon as they realize what’s going on? Anyway, to answer the original question, I don’t think there’s anything at all wrong with nursing in public. If the mom is comfortable with it, then by all means she should feed her baby whenever and wherever the baby needs to be fed.