#!/usr/bin/perl -w
use strict;
my %message_id;

while ( <DATA> ) {
    if ( /Email address:/ ) {
        print;
    } elsif ( /Message-Id:/ && ! $message_id{ $_ }++ ) {
        print;
    }    
}

__DATA__
Email address:     19324213@glerp  
Message-Id: <200103160515.WAA07878@mal.elp.rr.com>
Message-Id: <200103160515.WAA07878@mal.elp.rr.com>
Email address:     19075680@glerp
Message-Id: <200103150512.VAA27508@prxy3.ba.best.com>
Message-Id: <200103150512.VAA27508@prxy3.ba.best.com>