I was having a problem using SQL Server data transformation services’ database import feature. It appears that the problem was (found by my buddy and co-worker Rob) with the fact that I had a stored procedure that relied on a full-text catalog.
Since the catalog is not copied with the database, the stored procedure, that uses the full-text-search-specific predicate CONTAINS, caused the problem. Not copying it, solved the issue. I then needed to re-create the index and then re-create the stored procedure.