I added a second Weather Report applet, configured it and it worked properly. So, how to delete the faulty one? I couldn't right-click and remove it as it wasn't visible.
The panel's applets are represented in the file system in
and are (usefully) named applet_0, applet_1, ...
I could have opened each one's XML configuration file and examined it to locate the Weather Report applet but a quicker alternative was to run gconf-editor and examine each applet's configuration directly.
This also gave me the opportunity to compare the configurations of the working and broken Weather Report applets but other than their locations in the panel their configurations were identical.
It turned out that applet_13 was the the malfunctioning one, so I deleted it from ~/.gconf/app/panel/applets.