One myth I've heard a bunch of times from anti-prostitution campaigners is that something like two thirds of prostitutes enter the industry before the age of 14, or something equally ludicrous-sounding. I don't know where that number comes from, but it surely can't be right.
The problem with illegal prostitution and drugs for that matter is that since they are illegal a lot of other illegal activities come along with it. In the case of prostitution you have kidnapping, violence, and forcing people into underage sex (and from what I've read most prostitutes start very very early by being forced into it). If the girl is already doing something illegal and gets beat by her pimp what is she going to do? Pimps prey on this thought that there is nothing she can do.
Drugs are similar in that by making them illegal you bring in gangs, guns, and even move violence. If someones pot dealer screws them over what is their only recourse? Violence. You also have the violence of territory to sell on, etc...
IMHO, the illegality of things like drugs and prostitution actually causes the social effects to be worse then if they were legal.
I agree that social effects are probably worse, but making prostitution legal doesn't solve all of them - after all, underage prostitution will always be illegal (I hope) and probably rightly so, and that's one way into all those illegal activities.
Here in Uruguay, prostitution is legal, yet we do have problems with minors being pressed into prostitution, and also the sex export trade, where women are more or less kidnapped and sent to Europe (Italy and Spain mostly)
I doubt that it's true in America but the vast majority of prostitutes live elsewhere. For a poor person living in the 3rd world, you're probably not going to secondary school so you end up starting your "career" a little earlier. Also, consider differing ages of consent.