Who would grant `sudo` privileges to `www-data` without asking for a password? That's just asking for a bad time.
if their httpd.conf has incorrect privs set, you could run a script that changes the "user to run as" to root, then set up a script that would run on next reboot to apt-get upgrade and remove the root privs config line. you'd have to wait for the server to go down or reboot however long in the future, but hey it would work.
This is especially bad on systems where /bin/sh is /bin/bash, since /bin/sh gets invoked implicitly by system(3). So you could have a non-bash CGI program invoking a non-bash program using system(3) and you can be exploited.
The amusing up/down vote war I am watching on my karma gives me hope that at least 50% of HN got it...