Although it is standard practise to set the mode_param in your setup method, what you are doing is not wrong. So I would say that this is a bug in CGI::Application, and you should send it in (either through rt.cpan.org or send a quick message to the list at cgiapp@lists.erlbaum.net).

Update: An updated version (4.03) of CGI::Application which solves this problem is on its way to CPAN.