Created attachment 123304 [details]
patch (I'll remove the unnecessary printlns)

Looks ok overall, a few comments.

   1. You're doing:
iconUrl = new URL(base.getProtocol() + "://" + newHost + "favicon.ico");
and then a few lines after:
iconUrl = new URL("http://" + newHost + "/" + "favicon.ico");

I think you might need the extra "/" in the first case too. 

   2. It will be easier to read if you change the top level if statement from:
if ((defaultIcon == null) || (defaultIcon.getImageData() == null)) {
    ... try top host ...
} else {
    ... return non-null icon ...
}

to


if ((defaultIcon != null) && (defaultIcon.getImageData() != null)) {
    return defaultIcon;
}
... otherwise try to find in top host ...


   3. In getBugzillaIconImageDescriptor() you do 
  ImageDescriptor defaultIcon = ImageDescriptor.createFromURL(iconUrl);

  URLConnection con = iconUrl.openConnection();
  int len = con.getContentLength();

but in the original code they first opened the connection and checked the
length, and then got the full icon if not 0. Is there a reason you switched
them? Not sure if it makes a big (or any) difference but might be better to
check for 0 length first.

Created attachment 123316 [details]
Updated patch with Igor's suggestions and removed printlns.

I'm committing this.

As a result of the patch there's a problem with the Ubuntu bugzilla, adding
dependency on that bug.

Patch commited.