I would question the need to make the indexed view unique.  Is a regular indexed view not enough?

My biggest concern is when you attempt to insert a record into a table used in the view and the insert is rolled back because it causes a duplicate record in the view (but does not violate a constraint in the table itself).

If you must have a unique constraint, I'd recommend you enforce it at the table level.  If the indexed view must return unique data, use SELECT DISTINCT.   I don't think enforcing a UNIQUE constraint on an indexed view is a good idea.