Any used space that is not accounted for by GrandPerspective based on the size of all files it scanned is dubbed miscellaneous used space. Basically, it is unclear what is taking up this space. So if there is a lot of miscellaneous used space and you want to find out what it consists of, you need to scan more. More specifically:
First try running the app as a user with admin rights. You can see which users have admin rights in the "Users & Groups" System Preferences Panel. Log in as a user with admin rights and start GrandPerspective as normal.
If that still leaves too much space unaccounted for, you can try running GrandPerspective as root user.
Note, this is generally not recommended.
The app is not specifically designed for running as root.
It seems to work, but do so at your own risk.
Be especially careful when deleting any files.
Enough disclaimers, here is how to run the app as root user.
From a Terminal window go to the folder where the app resides and execute the following:
sudo /bin/launchctl asuser 0 GrandPerspective.app/Contents/MacOS/GrandPerspective
If after following all the above, you still have a large amount of miscellaneous used space, you can resort to other tools.
In particular, you can run the du command as root:
sudo du -xhd1 /
Here -x ensures only disk usage of the current volume is scanned, -h gives human readable output, and -d1 only displays one level deep.