I remember Fallout 2 had 2 bugs related to the ending sequence: no matter what you did, you would always get the "bad" ending for Vault City and Goris' brethren and Harold's tree would never really bloom. Also, in Fallout 1, there seems to be a glitch where Necropolis is always screwed up, no matter if you meet the conditions to save it.

It certainly was a bug, as I had checked some forums and walkthroughs and did everything that was required to get the "good" ending, but I got the "bad" ending anyways. I only got to see the endings I "deserved" on YouTube! So, do you folks know if the Fallouts provided here by GOG have had this fixed? They certainly don't look like "enhanced" versions in the sense of Beamdog's Baldur's Gates, which have several bugs fixed and some minor gameplay enhancements added.

No. GOG verisions are not "enhanced".
You don't get fixes beyond the latest official patches from Interplay, except for the better compatibility with new Windows revisions.
Those storyline 'bugs', which are actually bugs or incompletey developed features, are definitely NOT fixed here.
Some things you metioned above are not bugs either but depend on very very tight time intervals. Miss the hidden timer and you won't get good ending.
Install unoffical fan-made patches yourself. They fix most (but not all) storyline problems.

Thanks! I'll look for it! Baldur's Gate and even Witcher 3 mods enhance the experience so much.

As for Necropolis, I dug a bit more and it's really not a bug; it's just a VERY tight time interval you have to save the city. I think I got the impression it was a bug because, in my very first attempt, I managed to save it without even knowing this was a thing. Subsequently, I found it extremely hard to save it, so I concluded (wrongly) that it must be some sort of bug, especially as the dead ghouls are, indeed, glitched (they are shown in the process of falling on the ground instead of being actual corpses). Beginner's luck, I guess.

Also, thanks for the quick reply!!

Links for the unofficial patches with brief explanation are in that post. Well, yeah... That IS a well known FO1 engine bug. Game has internal limit for the number of simultaneously played back sprite animations. And script which kills all the Necropolis inhabitants at one timе clearly hits that limit. Thus most of the dead bodies remain in the "zombie" state. Unable to drop to the ground.

This is incorrect, the version of Fallout on the site comes with the high resolution patch, but does not come with the major restoration/fix mod/patch Fallout Fixt: http://www.nma-fallout.com/threads/fallout-fixt-next-release-will-be-some-time-in-dec-2019.194562/page-188#post-4307860

I'm not totally sure about the second game- but I'd be surprised if it wasn't a similar situation.

Would you, please elaborate on this high resolution patch bundled with a game? How does it works and looks? Screenshot would be appreciated.
Because the only non-standart thing I get from the GOG installer is ddraw.dll, which is an API-wrapper for modern DirectX. But it has nothing to do with high resolutions. And it's really doubtful that Mash's High-res patch could be incorporated into the commercial release legally.

There are two releases on this site: the original and the re-release. I can't speak to the latter but the original comes with the high resolution patch.

Oh. My bad. I have not updated my installer for ages. Yes, indeed now it includes HiRes Patch v4.1.8.
But I no longer can recommend original GOG release since it for some reason includes two incompatible fallout engine versions. Hi resolution version is 1.2, data files are from v1.2 too, but 'Classic Fallout' shortcut runs fallotw.exe v1.1. Switch from 'classic' to 'hires' and your saved games won't load. Switch from 'hires' to 'classic' and get unpredictable crashes with damaged saved games.
It has condenced font from european release as well. It's vital for WE languages with larger median word length but looks really not good with original american English. Looks like multilingual CD release was used as a base.

P.S. Even a launcher is glitchy...