A Quick Guide to Using Alternate-port SMTP with Exchange
This guide is for Exchange 2003. We don't currently have a guide for Exchange 2007, but a user has submitted the steps he took to get a working configuration. They are at the bottom of this page. Thanks to No-IP.com users Ernie and Francisco Thillet for the info!
Setting up Exchange 2003 to use Alternate-port SMTP is a quick and painless process. Basically three (3) items need to be changed in the Default SMTP Virtual Server and then the service must be fully restarted. Let's begin.
Open the Properties pane for the Default SMTP Virtual Server using the Exchange Manager

Go to the Delivery tab. There are three buttons at the bottom. We will need to make changes in the dialogs presented by each of these buttons. Start with Outbound Security...

On the Outbound Security dialog choose Basic Authentication and enter your username and password. This is the username that corresponds to your SMTP service and it looks like this: domain.com@noip-smtp. Be sure there are no extra spaces at the end of your username! The password is the password that you created on the No-IP.com website for Alternate-port SMTP.

Choose OK to close this dialog and return to the Delivery tab of the Default SMTP Virtual Server Properties pane. Click the next button, Outbound connections....
On the Outbound Connections dialog change the TCP port to 3325.

Choose OK to close this dialog and return to the Delivery tab of the Default SMTP Virtual Server Properties pane. Click the next button, Advanced....
On the Advanced Delivery dialog change the Smart host to smtp-auth.no-ip.com.

Choose OK to close this dialog and return to the Delivery tab of the Default SMTP Virtual Server Properties pane. Choose OK to close the properties pane.
Configuration is complete! But the service needs to be restarted in order for the changes to take effect. Stop the service and wait a little for it to shutdown completely. Then start it back up.

If you're not using a separate SMTP Connector on your Exchange server, you're done! Send a test email and watch your logs to see that it was delivered properly.
NOTE: If you're using an SMTP Connector with your Exchange server, you'll have to perform the following procedure as well.
Open the Properties pane for the SMTP Connector using the Exchange Manager

On the General tab, select the Forward all mail through this connector to the following smart hosts radio button and fill in smtp-auth.no-ip.com.
Next, go to the Advanced tab

Once on the Advanced tab, click on the button marked Outbound Security, select Basic authentication and then click on the button marked Modify

In the resulting Outbound Connection Credentials box, enter your username and password. This is the username that corresponds to your SMTP service and it looks like this: domain.com@noip-smtp. Be sure there are no extra spaces at the end of your username! The password is the same password that you created on the No-IP.com website for Alternate-port SMTP.

Click on the OK button in the Outbound Connection then again in the Outbound Security and the SMTP Connector dialog boxes. Your configuration is now complete.
These instructions have not been tested but have been reported to work.
Set-SendConnector -Identity "SENDCONNECTORNAME" -port 3325