The image should explain it; peek around the mouse pointer, certain minimap elements... I'm also getting extreme flickering but I've come to expect that from my hardware:
1.6ghz Intel Pentium Dual-core
Intel Graphics Media Accelerator (GMA) 965
Vista Home Premium
Tried fiddling with the options but I didn't have much success. Anyway, even the flickering and opaqueness isn't a deal breaker for me, but if anyone has any ideas of how to remedy it, I'd greatly appreciate the advice.
Personally, I blame the Intel graphics. It's easier that way and usually accurate ninety percent of the time.

Yeah, I'd probably blame the Intel graphics, too, LOL! They've never been that great for compatibility, especially on older, lesser known games. Usually need a GeForce or ATI video card for full compatibility.
Still, I can think of a couple things you could try:
First, try updating to the latest graphic drivers. Not sure whether you've got 32-bit or 64-bit Vista, so here's the links for both. If you don't know which it is, it's probably 32-bit:
32-bit Vista: [url=]http://downloadcenter.intel.com/confirm.aspx?httpDown=http://downloadmirror.intel.com/17119/a08/winvista_15114.exe&agr=&ProductID=2529&DwnldId=17119&strOSs=&OSFullName=⟨=eng[/url]
64-bit Vista: [url=]http://downloadcenter.intel.com/confirm.aspx?httpDown=http://downloadmirror.intel.com/17122/a08/winvista64_15114.exe&agr=&ProductID=2529&DwnldId=17122&strOSs=&OSFullName=⟨=eng[/url]
If that doesn't work, you can try disabling some of the hardware acceleration. To do that, go to the Control Panel, then Display, then click the "Settings" tab, then click the "Advanced" button, then click the "Troubleshoot" tab. Then you will see a slider bar where you can switch between the different levels of hardware acceleration. You can try the different options out but the one that should fix this particular type of problem would be one step below "Full." The description below should read, "Disable cursor and bitmap accelerations. Use this setting to correct problems with the mouse pointer, or to correct problems with corrupt images." Once you have this selected, click the "Apply" button, then the "OK" button.
Phew, hope that works for ya.

Oh! Thanks a ton for the advice! Hm, I followed you to the troubleshoot menu, but I'm told that my "current display driver does not allow changes to hardware acceleration settings."
Grah, blasted Intel drivers. I had just updated them, which didn't seem to help, though it did finally give me OpenGL 2.0 support. Sort of. I have bloom now, but bloom causes even a simple program to drop from 40+ FPS to... average 2.41 FPS. Handy! XD
Thanks a lot anyway though; that sounds like it would have worked fine for the cursor at the very least (which would have been more than enough!) but, it appears to be locked.

Bah... stupid Intel. Maybe older drivers would let you change those settings?
The only other thing I can think of is that, like some other games this old, they might have some command switch to turn off the hardware-accelerated mouse cursor. Something like -softwarecursor or -nohardwaremouse or whatever. But I have no idea what exactly it would be since I can't find anything online about it.
I think you're down to either directly contacting GOG.com support to see if they can help or getting a new GeForce or ATI video card.

Thanks! Yeah, I'll pretty much have to do that. I'll check for any software cursor arguments and such too. Thanks a lot for your help! I think this is officially solved.
No replacement card possible though; laptops. Gah! Still, the game is incredibly engaging despite this minor setbacks.

I seem to have wound up with similar hardware specs as the original poster, and not only do I have the same black box problem (no flicker so far, but I'm only in the tutorial levels), but I am also locked out of adjusting my hardware acceleration. I long for the days when I could afford dedicated hardware accelerator cards. Ah well. I'll keep fussing with it.

Has anyone found a fix for this problem?

Sorry for necromancy but I have the same problem, I've tried updating the drivers and running in various compatibility modes but nothing seems to help. Any advice would be appreciated.

Same problem here, also have an intel integrated card. I have the latest driver, so that is not the solution, despite what the SOLVED seems to claim :p

Same problem as well, although I am running Win 7 x86

I'm having the same problem, and GOG support had no idea how to fix it. Well, I shouldn't say that - they had a lot of ideas, but no solutions. Although to their credit, they tried pretty hard. =P
This shouldn't have been marked "SOLVED", I got all excited when I saw it and then got my hopes dashed on the ground. Also, that makes other people who might know the solution less likely to open up the thread.
-Gammix