Note to the lady with the screaming child: Leave Now.
I understand that you probably need groceries - that's why you are here. I even understand and can sympathize with your embarrassment as your 5 year-old takes items from your cart and throws them on the floor or at the shelves.
But just ignoring what the kid is doing isn't really teaching him anything. By pretending that what he's doing doesn't bother you, all you are doing is reinforcing the fact that there are no consequences for his actions. Taking him out of the store and away from the things he's screaming about will not only show him that he can't get away with acting like that in a public place, it will also help my ears and the ears of the other customers in the general area.
Passive Parenting doesn't work. I can't even begin to understand how people can feel that it's the way to go when raising their children. You have to react to what your kids are doing and saying. You have to show them where the line is between acceptable and unacceptable behavior. As much as I'd like to run SuperNanny's little British car off the road - I have to admit she's right.
People like my kids - I get compliments on them and their behavior all the time. Why do people like my kids? Because they are polite and well mannered, yet they are still kids. They aren't vicious hell-raisers and they aren't automated robots either. Do they try my patience? Oh God, yes, but that's why I'm their parent - they try my patience so that they don't do it to anyone else.
So reminder to the lady with the screaming child - I don't care what you do, as long as you do something.