Some time ago I installed a management server in a network different that the one where the Operations Manager 2007 database and root management server was installed. According to the guide I would need to open port 1434 between management server and database, 5723/5724 between management server and root management server and 1433 between management server and data warehouse.

But we also found out that when using named SQL instances you will need to open port 1434 UDP between the management server and the SQL database. In our scenario we used named instances on the data warehouse machine. The management server knew about it and tried to query the SQL Browser service on port 1434 UDP to get the correct network port for the SQL instance. Even if the instance is using the default port, the management server needs to query the SQL Browser service to get it. That query is sent on port 1434 UDP.