lopanhouki: I fixed it on mine by manually downloading the patch file. I got the link from one of the other threads on the front page. It won't let me create links so I will remove the https
cdn.gog.com/open/galaxy/client/2.0.58.4/setup_galaxy_2.0.58.4.exe
Had to exit GOG, install, then reboot the computer and so far no update errors. GOG would not launch until I rebooted. This was yesterday, so fingers crossed.
This helped me, no update popups since. But the client seems to take longer to start AND does not remember my login, even though i have "Keep me logged in" checked in settings. So...