I'm a fan of the original X-COM (even though I never managed to win a game), and I was pleasantly surprised to find this game on the Net. I installed the game from the installer posted on August 17, 2008. I have no problems on the Geoscape. However, I've been experiencing two problems that pretty much make the game unplayable.
I'm running a ATI Radeon X300 with the most recent drivers (8.8, update from August 20, 2008), a processor easily capable of running the game, and about 2GB of RAM. The game is having trouble displaying textures on 3D objects (such as weapons and personnel). This results in the game displaying the items with bizarre colors, to simply refusing to display them. I also have an absolutely crippling framerate in the tactical battles.
I don't know what additional information you require, but... e gad, this game is something I practically wished for, if it runs.