Hi I am having a problem with the game obviously. When I start the game the movies doesn't play normally; they seem to be corrupted. Also when I start a mission something similar happens. At first everything looks normal but then, when I move around the graphic seems to "overwrite" each other.

"Corrupted" how exactly? Can you take any screenshots of the problem?
The videos are limited to a 256-color pallette (common at the time the game was produced).

Color banding and a certain amount of artifacts resulting from quantization and limited bitrate are a normal result, but I'm not sure whether or not that is what you describe.
Compare with this video (set quality to HD): https://www.youtube.com/watch?v=eAv2D21kTIc .

I am having the same issues.

Sure; here some screenshot, first one is what video looks like, the two other is in game:
http://imgur.com/a/bpNXo

That looks like a scaling glitch. A resolution problem caused by what I have no idea.

This is the exact issue I had. For me, turning off DSR in the Nvidia control panel set it right.

Have you tried lowering or disabling DirectX graphics acceleration (if my memory serves, you can do that from DXDiag)?

I have DSR disable and I tried to force 640*480 without success. And I cannot disable hardware accelaration with the card I have.

edit: I thought I did it properly but I followed the instruction in the help outlet on GoG and it now work. So it was DSR all along!!