Instead of Apache::Error, you might consider CGI::Carp. This would have to be done at the script level rather than the server level. There is an option with CGI::Carp that will allow you to both display the server error reason on the screen in HTML and also e-mail the error to a specified e-mail address. For instance:

Contents of CatchErrors.pm follows:
-----------------------------------
use strict;
use CGI::Carp qw(fatalsToBrowser set_message);
use Mail::Sender;

BEGIN {
   sub email_problem {
      my $sender = new Mail::Sender({
        from => 'errors@yourdomain.com',
        smtp => 'smtp.server.com'});
      $sender->MailMsg({
        to => $Error::email,
        subject => $ENV{SCRIPT_NAME},
        msg => $_[0]});
      print "Website Error";
   }
   set_message(\&email_problem);
}
sub import {
  $Error::email = $_[1] || 'errors@yourdomain.com';
}

1;
--------------------------------------
Then, in your perl script, simply include the following line:

use CatchErrors qw(recipient@yourdomain.com);
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Using this method, you should be able to redirect all of the script's errors to an e-mail address you specify when you "use" the package.