I accidentally screwed up the folder permissions of the Magento root directory.
There is no harm in resetting the correct permissions. For more information on permissions you can consult the official website: http://devdocs.magento.com/guides/m1x/install/installer-privileges_after.html
You can use an FTP or SSH program to visually see what the file permissions are for the files and directories.
Note: I am not asking how to set the permissions. I am asking how to have Magento verify they are correct for me.
This doesn't exist, the purpose of this check during installation script is to ensure that certain directories have the right permissions so they can be written to otherwise Magento wouldn't load properly.
The correct method to address your situation is to simply reset the permissions.