Seems to me that Java's users are developers. No non-developer will ever install Java by itself, they'll only install it because something else they're installing requires it.
As a systems admin, I play mostly in 3, deploying, tuning, configuring, monitoring (to the extent that piss-poor Java tools allow any sort of monitoring -- want a dump of what's in memory? Sure ... let's just pause ALL activity on the VM for the next 25 minutes), troubleshooting, and patching/updating the VM.
I'm also concerned with the security model, within the parameters of my other system security concerns.
For the language and class libraries, it's largely ensuring that what my devs need and use is provisioned on our test, staging, and production hosts. There's also digging through some of the logging / crash / debug output to see if I can sort out what's wrong and fix it myself, or punt it over the wall to Engineering.