I was playing the Quake 2 Ground Zeroes expansion, but when I tried to load a save file it gave me an error saying the function pointers have moved. I thought I just happened to have stumbled across a random glitch, so I started over from the beginning. But when i tried to save and then restore again I got the same error on a new save file.
It seems that this is happening with all of my mid-level saves. (The auto save when I enter a new level seems to work fine.)

What is going on, and how do I fix this?

GOG wrong build game. And do not update since initial release, for unknown reason. Check game support page for 2 dll files that required for addons - GOGs put them only there.

The support page the above response is referencing, with the two DLL files - https://support.gog.com/hc/en-us/articles/115003255849--Read-Level-Error-Function-Pointers-Have-Moved-error-

Better buy game here AND on Steam - and combine them, using Steam version as base version (no files replace, only adding extra MUSIC and NETPACK folders). No GOGLauncher needed for that combo-version.

Also, since 3.10 patch game do not have DRM. You can install latest 3.20 update - it update also addons (GOG do not know that in 2012) to temp folder and replace dll files then in game+addons fodlers.