The applet drag and drop "Desktop Integration Warning" flashes behind the browser window when a tab is closed and when I bring that dialog to the foreground, I don't know what applet it is for because the Weather now applet is still buried.

Here is a use case that I think we should improve:
drag applet out
do stuff that buries the applet window
close the browser tab that the applet came from.
If I must be prompted now, I expect the dialog to come up right as I
hit close.
Instead, "Desktop Integration Warning" is flashing behind the browser,
and when I bring that dialog to the foreground, the Weather now applet
is not visible if it is behind other windows.

Per Ken R's response to my email:

The LocalInstallHandler code should probably be smarter and should raise its dialog to the front. Please file a bug against Java Web Start about this. If there were a way to get a callback from the LocalInstallHandler that it was going to raise a dialog, we could bring the applet to the front as well so the user could see it. You could include this in the bugs against both JWS and the plugin.

See email thread in comments.