Just as a quick note, I would do:

  my @addrs = split /\n/, $email_list;
  my @addrs_invalid
    = grep { not Email::Valid->address($_) }
      @addrs;

  print 'The following Email addresses are invalid:<ul>'
      . (map { '<li>' . $_ . '</li>' } @addrs_invalid)
      . '</ul>';
[download]

Untested and only proof of concept (no encoding and stuff), of course ;)