Error granting access to an App-V package: Invalid input was passed

Using the Microsoft Application Virtualization (App-V) Management Server website in an attempt to grant access to a package to an Active Directory group fails with the following error:

Invalid input was passed: contoso\appvusers. Specify a group as domain\group.

- OR -

Using the Application Virtualization Management Server PowerShell cmdlet Grant-AppvServerPackage in an attempt to grant access for a package to an Active Directory group fails with the following error:

PS C:\Users\appvadmin> Grant-AppvServerPackage -Name YourAppVPackageName -Groups contoso\appvusers

Grant-AppvServerPackage : An unexpected error occurred during processing.At line:1 char:1
+ Grant-AppvServerPackage -Name YourAppVPackageName  -Groups contoso\appvusers
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  
+ CategoryInfo          : NotSpecified: (:) [Grant-AppvServerPackage], Exception   
+ FullyQualifiedErrorId : System.Exception,Microsoft.AppV.Server.Cmdlets.GrantAppvServerPackageCommand

- OR -

Using the Application Virtualization Management Server in an attempt to add a user or group in the Administrators tab fails with the following error:

There was an error on the server. Please view event logs on the server for more information.

NOTE A corresponding event is not registered in the event logs

In each of the above scenarios, in a Fiddler trace you will see an HTTP 500 error. The error is listed as: 

The specified directory service attribute or value does not exist. ImproperADArgument.