Thank you for the feedback.
I didn't explictly test this script in a multi-domain environment. Within the script I am just using the identity information that is provided in the csv file. So the script user can provide any identity information that the cmdlet will accept to find the user.
UPN
Domainalias
Alias
So as long as script user provides the correct information in the CSV file to identify the mailbox to be moved the script should not have any issues with a multi domain environment.
My only concern with using option 2 would be that if the end user has modified the Search Scope using $AdminSessionADSettings it would not work in the expected manner.
Thank you for brining this issue up ... it is important that people using the script think about their environment and make sure they provide the correct information for the identity of the mailbox to ensure that they move the correct mailbox.
-Matt
Microsoft