Although those of you who feel entitled to tell others how to control their children probably won't understand or appreciate this, I will offer my thoughts on controlling/disciplining a child.
Many of you with more than one child know that each one is different. I have a 10 year-old daughter and a 4 year-old son. With my daughter, anytime she was testing her boundaries, a single-swat spanking would put her on the right track for a good, long while (like, for a month or two).
However, my son was born 6-weeks premature, has been diagnosed with various anxiety and hyperactivity disorders, and is just barely on this side of mild autism. When he is ready to test his boundaries, there is no amount of physical discipline that would correct his behavior (and, if I tried it in a checkout line, I'd have people griping at me for "abusing" my child). It just doesn't work. There have been a few times where I've had him with me, needed to stop at the local grocery store, and he has flat out lost it. No one has ever said anything to me, but I've gotten plenty of the looks you all have talked about. The thing is, as others have pointed out, I want him to stop just as much (more, actually) than you. There is literally nothing I can do at that point except to leave the situation.
Now, I'm not saying that the child in this incident has the same issues as my son. But, when I encounter an unruly child now, my wife and I exchange a knowing glance at each other and feel a measure of sympathy for the parent.
So, you all can now feel free to let me know that I'm just too soft, don't know how to parent my child, or that he just needs a swift "kick in the ass". Hopefully, though, this is able to enlighten some of you.