If you know that your child has a knack for getting into trouble, then I would suggest accompanying them to such public places. However, if you have brought up your child in the correct manner, and you believe they are sufficiently mature, then I see no reason to not let your child go to the mall on their own - maybe not at the age of ten, when the mind is still young and susceptible to manipulation, but 11 - 13 years of age would be a good start. It would teach the child responsibility and how to behave in public, as well as how to beware of shady characters. This would also be a hands - on learning experience, which I find more educational and valuable than some video, a lecture, or a textbook.
Perhaps between the ages of 13 and 16 that is the right behavior. But a child of 10 or 11 is in no position to be left alone with friends at the mall. Friends are not dependable at that age, and the child him or herself often has no common sense in order to avoid trouble.
I believe that young kids between the ages of ten and thirteen should not be dropped off at the mall without adult supervision. That is way too young. They can get into trouble too easily. Malls are also not meant to be babysitters. Kids should be at least 16 before they go to the malls by themselves.