Hi Andy,
It seems like the restore process did not work correctly or your db user is not in the dbo role so it does not correctly see the tables and stored procedures in the database.
When you move a site it should not run any upgrade scripts (you should not try to do an upgrade at the same time as moving a site).
What apparently is happening is it does somehow see the mp_Sites table (this is how mojoportal detects if it should be doing a new installation or upgrade), so by seeing this table it knows it is not a new installation so it then tries to check what current version is installed by running a stored procedure against the mp_SchemaVersion table, this apparently fails (either the user does not see the proc or table or they don't exist) so it does not know the version and tries to run the oldest scripts up to the newest scripts. But that is not needed and only causes more errors.
Hope it helps,
Joe