Since installing Lion, my son's managed account has been a disaster. I use Parental Controls to automatically filter web content. This has always worked well in the past. When he encountered a site that was questionable, Snow Leopard asked for my credentials to add it to the approved white list. This includes all secured (https://) web sites, which Parental Controls consistently and intentionally blocks, because the browser/OS can't appropriately filter for content on secured connections.
In the modern age of web browsing, however, hundred of companies attempt to install cookies, use invisible images (or other "bugs") or otherwise track Internet usage to sell to marketers. Many of these cookies and bugs make secured (https://) calls to their host domains, either to secure the user's personal data they are transmiting (probably their story) or to hide the information they are transmiting so we users won't know what they are tracking about us (probably the reality).
Either way, every time my son visits a web page from any even remotely popular site, a dialog box with a laundry list of of secured domains he has (in Safari's words) "attempted to access" appears. Dismissing the box is not helpful. Another appears every time he moves to another page. It is an incredible annoyance for both him and me.
I've blocked cookies from most sites in the Safari preferences. I've installed the Ghostery extension to block most of the "secret" marketing related traffic affiliated with most web pages. (I swear, if most people saw how many third-party companies track their private Internet browsing, they'd probably suffer anxiety attacks and never use the Internet again.) The problem seems a little better, but still isn't totally gone.
Any suggestions would be most welcome.