I believe I've found a solution to the stuttering mouse, which has annoyed me a lot up until this point.
The funny thing is, the solution doesn't seem like it 'should' do anything; but it works for me, so maybe it will for you too.
Locate the GOG folder containing the Populous The Beginning Folder. (Mine is Program Files x86/GOG.com)
Right-click > Copy your Populous 3 folder
Right-click > Paste it in the same GOG.com folder
You will now have a Populous 3 and a Populous 3 - Copy folder.
Go into the Populous 3 - Copy folder, Rightclick GOGSetup.exe and create shortcut to desktop.
Launch game from that.
It seems so stupid, but it's working for me. And any time I try to launch from the old folder the problem is back.
So for whatever reason, it works.