I recently installed my first Exchange 2007 Server and I had problems with recieving mail and found it to be related to the recieve connector.
Exchange 2007 have two kinds of connector. Send connector and recieve connector.
The send connector is located on the Organisation Level and you need to create one for the servers to be able to send mail to internet.
The recieve connector is located in the server level. The Default Recieve Connector is automatically created.
Note: By default it is set up to only recieve mail from authenticated servers. This is a problem if the server is connected directly to the internet. To fix this open properties for the Default Connector and go to “Permission Groups” and click “Anonymous Users” or use Powershell:
set-ReceiveConnector -identity “Name of Default Connector” -PermissionGroups AnonymousUsers