ERROR 1370 (42000) alter routine command denied to user
Most likely your Craft install has some custom stored procedures in it.  I say custom because Craft doesn't use them by default and therefore doesn't require the necessary privileges to use them.

You'd need to make sure the MySQL user account Craft is running as and the one you're using to import the database backup has the 
ALTER ROUTINE and CREATE ROUTINE privileges to properly use them.