We've already covered how Facebook's new Graph Search feature may cause some privacy concerns for some users. It's not that Graph Search allows people to see any more of your information than is already available, but it does make it much easier to find.
The fact that users can search parameters involving "people who like ______" and "photos of people who like ______" makes some users uneasy. But the bottom line is that Graph Search only allows people to unearth information that's already public. Sure, it may be tedious to go back and tighten the security level of all of your photos, posts, likes, etc. - but the point is that it can be done. Sure, Graph Search could lead to some interesting situations, but Facebook gives you a way to take yourself off the grid - if you so choose.
Anyway, privacy concerns are always magnified when it comes to kids, and Facebook contains a whole lot of kids between the ages fo 13-17 (and plenty under the age of 13 as well).
So Facebook has issued a statement on minors and Graph Search, seemingly in response (or preparation) to these privacy concerns. The main point is that Facebook doesn't treat minors any differently in Graph Search than it does in any other facet of the site:
As with all of our products, we designed Graph Search to take into account the unique needs of teens on Facebook. On Facebook, many things teens are likely to do - such as adding information to their timelines or sharing status updates - can only be shared with a maximum of Friends of Friends. In addition, for certain searches that could help to identify a young person by age or by their location, results will only show to that person's Friends, or Friends of Friends who are also between the age of 13-17.
Facebook's Minors & Privacy help page indeed confirms that Facebook only allows those aged 13-17 to share photos and statuses with friends of friends, and only friends of friends can tag them in posts. For minors, location services are also turned off by default.
You may disagree with Facebook's policies toward minors and think that even sharing with "friends of friends" is too much, but that's the overall Facebook policy when it comes to minors - and always has been. It's not an invention of Graph Search.
Of course, all the has to happen to get around all of these restrictions is for a kid to lie about his/her age. That happens all over the internet. And short of implementing impossibly resource-intensive and expensive mechanisms, there's not much Facebook can do about that.