I don't have Galaxy and I don't know anything about meddling with programs. I just download from the offline installers, install, and play. And I have noticed occasionally, while I was performing the installations, some error messages about missing files in different games. Usually you are given a button to ignore and continue installation and the installation could run until the end! But then the game either didn't start or start but having other problems, like a loading freeze. Most recent example for me in the latter, Syberia 3.

^ This. Or download each installer file via browser, and download the xml files for each separately as well. It only requires copying the still-fresh download link and adding .xml on the end. The xmls contain the MD5 checksums, amongst other things. (which Timboli likely knows, I'm just adding to his suggestion list)

Well, games are not supposed to work if files are missing, so that thing with Syberia is not much of a surprise.

But missing files during an installation ... that's very strange indeed. Bad downloads would result in different errors, as far as I remember (only had that once). The downloaded bin file would have to be named to be corrupted.
I used to download the installers using a browser as well and never had problems (it's just a lot more convenient using the script, since I own a lot of games and I can do that without sitting at my computer).

My point. randomly damaged files are let's say: unlikely to test okay.
Verify did not complain. Completed 100% without error. So something about the process is not working properly or I got a bunch of 1 in what was it, 4 billion?* Error that created a MD5 collision.

*It has been over 10 years since I properly looked into MD5.

edit:
Just got another Idea, best gues so far on how this could not be a mess up on CDRs side:
hardware bug Threadripper the early ones have a few known problems, maybe it affects something specific to instructions regarding MD5.
Everything is more likely then a bunch of random collisions. That's why I did not protocol anything. Failure simply did not make sense after all checksums passed. I dismissed the errors later during install as mislabeled warnings since the installer just continued.

Might not be your night to do the lottery then...

I do think that something is wrong on your end interfering with the download process. It's not common to get so many download errors.

I remember years and years ago when downloading large files over dialup using a downloader that would resume downloads from the byte count minus a certain margin - the implication being that whatever caused the download to fail might have also corrupted the download byte-stream. Not sure of the efficacy of this or whether it would be applicable to downloads nowadays.

I use gogrepoc which works well and has download/verify functions piggybacking off the offline installer files and the GOG API, such that there is. I have never used Galaxy as it is not necessary for me. Most installers I use are Linux installers which don't include the verify file functionality - but from gogrepoc it is unnecessary.

It appears that you don't understand what I said.

There are two types of MD5 to check.

1) The single MD5 value for an Offline Installer file (EXE and BIN). This is a package type file, containing many other files.

2) The MD5 value for each individual file inside each package type file. This can be in the thousands, and is partly why installing takes so long. These are only checked during install, and is not an integrity check of the whole package, just each individual file inside it.

The single MD5 value is produced AFTER an installer file is created, and includes a broader verification. Whereas the MD5 values for each file inside the installer file are produced during installer file creation, and added to the package at the final moment of creation.

Galaxy etc check the single MD5 after downloading each Offline Installer file. The individual files inside the Offline Installer file, only get checked during installation ... or if installing via Galaxy on-the-fly (no Offline Installer).