If you configure search scope based on some managed property (e.f. ContentType) via PowerShell using New-SPEnterpriseSearchQueryScopeRule cmdlet, e.g. using the following code:
You may get the following error:
Property "ContentType" does not exist
In order to fix it go to Central Administration > Service applications > Search service application > Metadata properties > Edit "Content type" property (or property which you use) > Check checkbox "Allow this property to be used in scopes":
After this New-SPEnterpriseSearchQueryScopeRule cmdlet should work successfully.