I found a bug in the explorer demo. When I deploy the demo on my local tomcat server and trying to go to "Async Tree", I have the following exception :
Caused by: java.lang.NullPointerException
at com.extjs.gxt.samples.explorer.server.FileServiceImpl.getFolderChildren(FileServiceImpl.java:57)
files = root.listFiles(filter); returns null if the absolute path of the tomcat server contains a space character (i.e. "Program Files"...). I don't know why. As a workaround, we can of course move tomcat to another directory.

By the way, I think there is a bug in the build.xml files in the SVN repo : I guess
debug="${javac.debug}" debuglevel="${javac.debug}"
should be
debug="${javac.debug}" debuglevel="${javac.debuglevel}"