Hello fellow old school gamers!
I am having a problem when trying to play DD on my Mac using Parallels 5 and a virtual windows 7 64bit os.
The graphics are full of black boxes around objects, and som objects are just empty black boxes. Everything else works fine, so it´s only a graphical issue.
Anyone having the same problems? Anyone have any solutions?
Usually I play games on another windows computer, but right now Im on vacation with just my Mac.

I'm not the one to give you any advice on Mac's or Parallels 5 since I have neither but . . . I can offer this advice for Win 7 64 . . . =)
You may have done the following already but I'll suggest these possible fixes. . .
First I would try this . . . right click the game shortcut, on the resulting dialog click Properties, click the Compatibility tab, check "Run this program as an administrator". You can also set a compatibility mode on this tab as well. I usually start with none and, if needed, start with the newest mode and work backwards till I find newest mode that works best with the game. Try playing the game.
If that doesn't help, I suggest backing up any saves you have, uninstalling the game and reinstalling outside of Program Files as described below -
Backup your saves, uninstall the game, deleting any directories / files that are remaining after the uninstall under Program File\GOG.com\Divine Divinity.
Turn UAC to Never notify.
Create a directory outside of Program Files, something like C:\Games. Right click the setup.exe and click "Run as an administrator" in the resulting dialog . On the first dialog of the GOG installer, click the Options button on the lower left corner and point the install to the Games directory.
After install, right click the game shortcut, on the resulting dialog click Properties, click the Compatibility tab, check "Run this program as an administrator" and uncheck the compatibility mode. You may need to use that but I would start without any compatibility mode selected.
Set UAC back to it's default setting. Try the game. This will at least eliminate some issues with Win 7.

This thread looks like it might be helpful for your problem . . . =)