Took the Mac Mini back to the Apple store. Their Genius said he was sure it was Virtualbox causing the problems, because all the kernel panics named VBox. (currently 4.1.2, most recently with 5GB RAM, OSX 10.7.2)
I'm dubious as I've had other crashes, some with just 2GB installed, that did not leave any log file, so I asked them to do a hardware stress test on it overnight.
EDIT -- they say nothing wrong with the hardware and blame VBox, because the VBox "kext" file is listed in everything that's been a problem. I do see in verbose logout that the Mac has trouble unloading a VBox kext file every time it shuts down, if that's a clue to anyone.