So, how do you deal with this? I haven't updated the game since summer. Now I decided to play, and this is what happened.

From my experience, the bug where textures are replaced with black and white squares occurs when the maximum texture size (quality) is set. Other settings don't matter, and if the graphics card is weak, you can set it to minimum or maximum... it doesn't really matter.
Apparently, the low-resolution texture pack is either missing or has errors, or the issue is caused by installing the game after/on top of the demo, which leaves traces in the registry/settings.

Good luck with the game :)