It's been exactly three years since I wrote Apple's iPhone parental controls are completely broken.
Sure, you could turn off Safari -- but there was no way to disable use of webkit embedded browsers. A lot of apps and games kids like, including encyclopedias, use links that bring up an embedded browser. From there it's often a few hops to Google and beyond.
I ranted about this in various places, but mine was a lonely voice. (One can imagine many reasons why most parents don't seem to be concerned about full web access with iOS devices, but, whatever the reason, there's clearly no clamor for a fix.)
Today, years after I gave up, Apple fixed parental controls in iOS 7. You can use Restrictions:websites:specific websites only to restrict both Safari and webkit access to urls. I believe the changes were made pretty deep in the iOS network stack, they seem to affect all browser use.
iOS comes preconfigured with a set of approved sites. The list is not simple to edit but they are all fine with me. You can add others.
There are bugs. Even preconfigured sites seem to sometimes require second authentication on attempted access. Still, it's a big, albeit very late, improvement.
IOS 7 is quite slow on the iPhone 4s two of the kids use, but this one feature is worth the sluggishness.
Update: In early testing #1 says he can't hack the current restrictions. It also seems to be far more useable than superficially similar site restrictions in OS X Mountain Lion; Mountain Lion's current mechanism has been completely broken. I wonder if some serious attention went into making this work.
Siri: "Show me pictures of dogs". Shows dogs.
Siri: "Show me pictures of xxxx"....
You have to disable Siri, there are no parental controls there.