Workaround for the AMD CrossFire that works for me:
Rename the Crysis2.exe to Cry2.exe (in the bin32 folder in the installed directory) and then run the executable with the new name.
What I think is going wrong:
AMD detect Crysis2.exe and apply some optimisations in the driver. These optimisations work for the demo, but the release .exe is different and the optimisations break the rendering on CrossFire.
However, I cannot guarantee this will work for everyone. AMD should be working on a driver/profile fix as I type.
Tried it. Lots of missing textures for me...nifty little wallhack, tho