I bought the "white label" retail version published by GSP a few years ago. Occasionally the screen will go black and you'll have to mouse over the whole screen to get rid of the black, like you're manually erasing in MS paint. Does the GOG version suffer from this as well?

I don't have the the GOG version, but there is a user made patch to fix that issue (I had it as well). It's basically a constant screen refresher, don't remember where i found it the first time around

I think I'd had that error crop up once but that was whilst I was playing that & tabbing back to the dsktop a lot to check emails & the like, I just put it down to that

It is superior, you will want to mod it, because that error happens with the GOG version, but with the white label copy, do you get a copy of the fallout bible, or the soundtrack of the game included as well?
IMO GOG version is far superior.

i did got the same error while playing with the "fixes" listed in the fallout 1 faq but not without them.

I have the GSP version and still have yet to get Tactics to work. I'm just way to cheap to buy a game I already own...despite the fact it doesn't work.
And I get that black over the screen all the time as well.
One day I'll just hand over the $18 to get the trilogy again...