I got the mac to display, and it's cheerfully downloading a bunch of software updates as I type this. The fix? A cheap Belkin DVI-VGA adaptor. Looking at the back the two adaptors, I see the problem - the Belkin one has far fewer pins on the DVI side. I tested three monitors against the mini with the Apple provided adaptor - zip. No signal to the monitor registered. Plug in the Belkin adaptor - it just worked.
So this is a pretty bad thing for Apple, IMHO. The OBE (Out of the Box Experience) for me was pretty bad, and I had to spend extra money to get the thing to work. Not a lot, but it's like sub-par service at a restaurant - it starts you off on the wrong foot. We'll see how the rest of it goes.