The patch checks the registry for the game's install path and version information and can give an error if it doesn't find the expected information.

As bengeddes said, there shouldn't be any saved game compatibility issues going from the previous GOG version to the new one. There were issues with going from the disk version to GOG, or less so from disk to Steam version (which is what the anthology version is based on). The uninstall program should ask if you want to keep your saves, but to be safe you might want to zip them or move/copy them to a different location, first.

Each save is a separate subfolder in the '..\Divine Divinity\savegames' folder. Under Vista/7, depending on how the user accounts are set up, if you install the game to the default Program Files path, Windows can create separate savegame folders for each user, and then map that folder to the game's savegame folder (so it will just see the saves for the relevant user).
C:\Users\ %account name% \AppData\Local\VirtualStore\Program Files\Divine Divinity\savegames

Shortly after the Steam release Larian said they would look into the music bug and other issues that were reported, but AFAIK there has not been a list of bug fixes released (haven't installed it yet). Unfortunately, this doesn't really sound like an issue that could be written into the save, so wouldn't hold out much hope a new game would work...