My patch to add fullscreen support to JOSM has been commited to trunk
There are some caveats with it as Java's setFullScreenWindow doesn't work properly on all platforms. Maybe I'm doing something wrong, but in the meantime it works on Ubuntu 8.10 under Compiz at least.

Discussion
Comment from kaerast on 18 March 2009 at 17:21
Cool! Shame it's not working with Open JDK without Compiz though.