Good news. On Macs and some new PCs, one can boot either in EFI mode (EFI being new replacement of legacy BIOS) or in legacy BIOS mode. I found out that if I boot from an USB I can only boot in EFI mode. Booting in EFI mode is known to have issues with certain linux video drivers - in particular nVidia chipsets don't work well when booting in EFI.

I therefore burned a CD with 12.04.1 amd64 and booted it in BIOS compatibility mode (http://dustin.li/2011/05/how-to-inst...on-a-mac-mini/). This worked well and I could boot 12.04.1 all the way into the Unity desktop.

BIOS compatibility mode offers good graphics performance so I'll stick with it and try to proceed with fresh install. Let you know how it goes.