This is how I test:

 - tomcat_stop.sh
 - ant deploy
 - tomcat_start.sh

In the browser, go to http://localhost:8080/echo

You can check the server side log files in $CATALINA_HOME/logs/catalina.out.

Log4j output from the servlets is in ~/Users/terri/cipresweb.log.  (If you aren't me,
change the log4j.properties file!).

Client side log (on the mac) is ~/Library/Logs/Java Console.log

When you change any of the jar files for the applet you need to make sure the browser 
downloads the new versions.  Rrun the "Java Preferences" utility, 
and on the "General" panel, under Temporary Internet Files, press "Delete Files ...".  
Then restart firefox (don't just close the window, quit the whole app).

Can also try to clear Mozilla browser cache: Tools/Clear Private Data, and restart browser -
but I haven't seen this work as reliably as using the "Java Preferences" utility.

Depending on changes made, you may also need to reload/refresh the page in the browser.