I just installed a Debian system on my son's laptop. I'm trying to work out the kinks, but there are probably some that I'll miss until he's 250 miles away at college. He's totally unqualified for root access. I'm not that great, but at least I know enough to be careful.

Here's my question: Is there a way I could connect to his computer thru the internet, log on as root and do program installations or other maintenance?

vnc will make it easy for you to do installation and other configuretion. For vnc to work, your son need to install vnc server and configure it properly and then you can use vnc client to connect to his computer (im affraid your son need to do some configuration OR you can ssh to his computer and install it yourself) also lookat "TIghtVNC" its usuallly installed in most linux machines (kmenu->internet->remote access)

webmin is another webbased tool for configuration and admin tasks. very simple to install, start the webmin server and ( if behind router, enable port forwarding ) remote login.

another simple way is to use "ssh" and if you need graphical display use X forwarding here is tutorial for reference