It wasn't designed to support parental control and supervision, but Google's new email delegation function is very helpful (emphases mine) ...
.... Administrators must first enable mail delegation by checking the 'Mail Delegation' checkbox under 'Email Settings' in the administrator control panel.
To enter a delegate, users can select the 'Accounts' tab under 'Settings' in Gmail and click 'Add another account' to enter their delegate's email address.
Once the delegate is signed into their own own Gmail account, they can then access the other person's account from the account selection menu at the top of Gmail....
You can only add delegation accounts that are a part of the Google Apps domain, you can't add external Gmail accounts.
It takes a while for the "account selection" menu to appear. About fifteen minutes after I set up delegation on my son's account a small arrow appeared to the right of my bold email address on the top right of my Google Apps Gmail page.
In fact currently my son does not directly use Gmail, it's just an IMAP service for OS X Mail.app. Only I know his Gmail password. So this doesn't let me do anything I couldn't already do, but it's much easier to monitor his account.