I was playing my new Unreal 2 from GOG and after the first mission, the game crashes. There is no name of the error or anything. I am playing it on notebook with Windows Vista installed. The game crashes right after the first mission ends.

Well, the solution was easier than I thought. I just needed to install up-to-date video & audio drivers and the game runs just fine.

Hello,
I am experiencing the same issue. I am using Win7 64-bit RC. I have the newest possible stable drivers from Nvidia installed. Also the newest sound drivers for my SupremeFX oboard sound card. I've found this in Application Event log:
Faulting application name: Unreal2.exe, version: 0.0.0.0, time stamp: 0x21544c46
Faulting module name: dmusic.dll, version: 6.1.7100.0, time stamp: 0x49eea50c
Exception code: 0xc0000005
Fault offset: 0x0000fb6b
Faulting process id: 0x12f0
Faulting application start time: 0x01c9f831c2c0b6eb
Faulting application path: C:\Games\Unreal 2 – The Awakening SE\system\Unreal2.exe
Faulting module path: C:\Windows\System32\dmusic.dll
Report Id: 7fd16df7-6428-11de-a8cc-8000600fe800
It looks, that issue is caused by sound drivers/DirectX. Hard to say.
Joe
edit:
i've found newer sound drivers, will see if the creashing stops
edit2:
looks like new drivers for sound card resolved the problem