Since posting this, I did some research, and it looks like the biggest security problem (currently) is manufacturers hardcoding default passwords into the firmware. Here I am thinking I need to become an expert in security to help my clients secure their devices, but is it really as simple as encouraging clients to set secure, default passwords?
Unique passwords for each device, some form of auto-updating so the OS and any webservers don't get too old and making sure the developers know about the OWASP Top 10 should go a long way to making the devices secure.
Anything else would be dependent on what the device is for and how it does it.