The health dashboard is what I use to quickly see if there are any current issues. You can also setup the system to email with alerts for any problems that show up in there. Previous to that feature, I would look at the ims.log to see if it was complaining about anything.
To diagnose problems, it depends. Most of the issues we encounter are failed endpoints. Either software bugs that require a reboot (possibly followed by a firmware upgrade) or flat out hardware failures. Occasionally, customers will introduce firewalls into the path or other network elements that can cause issues and we have to dig deeper. On a typical system, its usually the endpoints, in my experience. Just my 2 cents.
Vance