My site is pretty large and I use a caching system (JRE cache extended) to make it even half-way manageable. The caching system uses full page caching, so if the page is viewed first in a browser, the plugin detector for mobilejoomla doesn't work.

You can set certain php or js files from not getting cached, or you can set cookies from being cached. Any idea how to make mobilejoomla work with a system like this?

I have the same problem. My site is working with System Cache Plugin native of Joomla turned on, so Mobile Joomla don't work well. So, It' works perfectly with Cache turned off, but then my site is slower.

I've found a post that would be interesting for developers:
forum.joomla.org/viewtopic.php?p=1710191

Greetings.