The problems (described here)
with textures being distorted in a way that they seem like there's a second transparent layer copied over it that shifts and moves as the camera moves, depending on distance, lighting and probably several other factors, are most likely caused by the 1.0.2 patch.
I updated my Catalyst Control Center and all drivers, spent an hour turning all kinds of settings on and off in both the game and the Catalyst Control Center until I finally remembered that I had no problems like this in the original Penumbra Tech Demo or the Overture Demo.
I reinstalled Penumbra: Overture and didn't apply any patches and voila, no graphics problems whatsoever. I did, however, began experiencing the menu lockup problem when hitting escape in the game again, pretty much like in the demos.
Anyway. Perhaps studying the 1.0.2 patch could give some answers, obviously it fixes a lot of bugs but for some reason creates a new one.