I would like to get JME to output logging messages to a GUI window instead of the console window. Have you tried this already?
The logging system seems to be pretty complex, so some tips would be appreciated.
Perhaps you could create your own java.util.logging.Handler object (see Logger.addHandler) to listen to the logger and repeat the log messages in your AWT/SWT interface?
I missed this message…yeah, what Renanse suggests is the right way to go…I've done this myself (for a non-game project).