I just did a clean install of the GOG version on my Win7 system (Nvidia Geforce GTX 750 Ti). Almost everything seems to work fine, except certain textures allow me to see through walls/floors/objects, and I get screen tearing (I think that's the right term) when looking at a view of open space/stars/night sky -- but not other skyboxes, like on the Bespin multiplayer map. See screenshots.

I tried using the Nvidia settings to force Vsync both on & off; neither made a difference. I also messed around with the game's screen resolution, backbuffer, brightness, view size, and min texture size, but those didn't affect it either. (Turning off 3D acceleration made everything turn fluorescent colours.) I've also attached a screenshot of my 'normal' graphic settings.

Any ideas on how to fix this?

You could try using the JkGfxMod.
Here you can find the installation guide. Note that you will need the original executable file which can be obtained using the jkversions utility.

An alternative solution involving the unofficial patch and the dgVoodoo wrapper is to follow this guide.

Thanks. It gives installations instructions for the CD-ROM, Steam, and GOG Galaxy and versions, but I'm using the "regular" (non-Galaxy) GOG installation. Which instructions should I follow?

Ugh, now it's suddenly crashing as soon as I load a level -- and I didn't even change anything!

Sorry about that, even supposing that you have installed it correctly, I'm not sure if that mod is completely compatible with Windows 7.

At this point I suggest you to completely uninstall the game, reinstall it and the follow the other solution I suggested: dgVoodoo is compatible with Windows 7 and should solve any graphical issue with the game.

No, I hadn't made any of the changes you suggested yet -- I just started it up with exactly the same installation/settings that I was using a week ago (which had worked, except for the graphical glitches I mentioned)..

I tried doing another clean install, but it still doesn't work.

Those glitches are very severe and proved that the game wasn't stable at all, even when it used to run, hence I'm not surprised that the game is crashing now even if you haven't changed anything. As I said, the game is unstable on modern systems. You could try setting it to run in compatibility mode for Windows XP, but the better solution for you is to use dgVoodoo, as I said in the previous post.

I tried the "other solution" (The Unofficial Patches) and they made things worse -- the game crashed in the same way when launching the game itself, instead of making it to the menu and lasting until I tried to load a level, as before.

In both cases, it crashed in the same way: I would get a black screen and hear a split-second of the game/cutscene audio, and then the game would minimize itself, while a black window for GOGLauncher.exe stayed on the screen. When I clicked on the game's button to restore it, it usually crashed, but sometimes it would just re-minimize and I would eventually have to close it manually.

Have you installed dgVoodoo as written in the guide?

Yes. It also crashes when I load a level, identically to when I used the vanilla GOG install.