Here you will find some notes about Javascript and Applet integration in various browsers/OSes.

Tip: Tracing and debugging applications in Java Web Start and Java Applets

Firefox

JSObject.call() does not work

IE

Javascript calls to applet methods are executed unprivileged (the whole stack). In the applet, wrapping privileged code with:

AccessController.doPrivileged(new PrivilegedAction() {
  public Object run() {
    // do priv code here
    return null;
  }
});

Safari

Javascript can only call methods on an applet when the page is served from the same domain as the applet jars.

Chrome

Not tested...