I did update and upgrade before running the ISPConfig update.
I can no longer get shell access to my box - Putty comes back with "Server unexpectedly closed network connection". Nor can I FTP to it. I could do both of these things even after the mail issues started.
I can log into ISPConfig and the box is not full:
Filesystem Size Used Avail Use% Mounted
/dev/sda1 49G 6.4G 40G 14% /
tmpfs 256M 0 256M 0% /lib/init/rw
udev 256M 464K 256M 1% /dev
tmpfs 256M 0 256M 0% /dev/shm
and all services are running. I think I might have to do a restore back to before I ran the Debian updates.