IIS > SharePoint Web Services > (applicaiton) > Basic Settings > Test Settings
Results in an Invalid Application Path error message.
When The server is configured to use pass-through authentication with a built-in account to access the specified physical path. However, IIS Manager cannot verify whether the built-in account has access.
You see this error message (actually it is a warning message) because you have choose to use pass-through authentication. In this situation, the application pool is run under a low-privileged built-in account, usually Network Service, or ApplicationPoolIdentity. IIS cannot verify that the built-in account has proper settings, this can only be done at run-time.
In addition to this, the "Test Settings" process does not know which user you have authenticated as. So basically, you need to verify that the application pool identity has read access to the files and configuration files. You also need to make sure that the application identity has proper security settings.
So in most situations, you can safely ignore the warning message, because on a default setup, all the permission settings are correct.