Crysis and Crysis Warhead DO NOT support NVIDIA PhysX GPU acceleration, so turn it off via NVIDIA control panel if you've got it. I have a GTX 295 card on Win7 64-bit (DX 11), and Crysis had degraded graphics with PhysX enabled. Transparency is all messed up (e.g. burning embers and other things like the alien in the transport crate you are chasing (Warhead)) and also there is strange flickering and degraded shadows if PhysX is enabled. Turn off PhysX for Crysis!!!!!! This had me quite frustrated for a few days until I figured it out.
My problems started after installing the latest NVIDIA driver, version 195.62. Rolling back to 191.07 fixes all problems. I searched the web and othesr are having problems with the latest driver as well. With 195.62, Crysis/Warhead have major problems. So, the problem may not be related to PhysX, but as Crysis doesn't support its use, I'd still turn it off.