Unless you start messing around with print (which I wouldn't recommend until you understand CGI::App more), CGI::App will only display what you explictly return from a runmode.
So to show the results of another sub that your runmode calls, you need to get it's results into your runmode's return:-
# Perhaps like this...
. "here2: " . Dumper(@errors);
# ...or this...
my $errors = errorhandler(\@errors);
return $errors . "here2: " . Dumper(@errors);