Although I haven't been blessed with children yet, I was helping my neighbor the other day who has a bundle of them. She wanted to set up Parental Controls, which worked great, except as soon as the internet filter was turned on, Gmail broke.
The short explanation is that the filtering also filters secure communications (i.e., https), but it's buggy in the current version. I couldn't find any fix, but there's a pretty easy workaround: just add any secure websites you want to access to the "Always Allow" list (under Customize). For example, to get GMail to work, just add "google.com" to the Always Allow list.
The filtering still works pretty well, considering most children probably aren't going to many different secure websites.
[robg adds: I haven't tried this one.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=2009010522201161