In general, it is not advised to have a server listening on multiple ports. The port settings for Geoserver, running under Tomcat, are set in the
server.xml file, which in my setup, is located under
/etc/tomcat6/server.xml. Open this, find the connector port, change to 80, restart tomcat, eg,
<Connector port="80" ....
As the port is set under Tomcat, not Geoserver, if you want to run two instances of Geoserver on the same machine, you will need to set up two version of Tomcat, one listening on 80 and the other on 8080, and then deploy your Geoserver.war file into each one separately.