The game demands a graphic chip that supports OpenGL 3.0 or higher. That's sometimes not the case especially with Intel integrated graphic chips.
In case you're using one, check Wikipedia if yours supports OpenGL 3
http://en.wikipedia.org/wiki/List_of_Intel_graphics_processing_units

I'm using Nvidia GeForce 9500 GT.
According to Wikipedia it supports OpenGL 3.3.

Do you have a second graphics chip, e.g. integrated in an Intel CPU. I'm asking, because most of this glitches are connected to Intel Graphic chips. If so, make sure the game uses the GeForce.

If not, this will get tricky. Definitely update your Nvidia drivers and set all it's settings back to default.
You might also want to contact the game's support directly: support@facepalmgames.com

Yes, I have a second graphic card integrated into motherboard. How do I do this?

There's no standard way, but a good start is to go to Nvidia's control panel and look at the 3D settings.
If I remember right, there is an global option to always use the Nvidia card by switching from Auto to Nvidia.
Reboot your computer afterwards.
If you just want this game to use the GeForce you can save settings for specific executables.
I'm not at a computer with Nvidia hardware right now, so I can't give you an exact step-by-step.
But a web search provides tons of links. This one might be helpful:
http://www.howtogeek.com/175281/how-to-force-graphics-options-in-pc-games-with-nvidia-amd-or-intel-graphics/