The problem is in the postfix increment operation.

$H_count ++ and print ' On List H' if exists $H_list{$_};

Use an if block (or similar) instead to avoid conditional dependence on $H_count under the increment operator. Others will be able able to explain the reasons in detail.

use strict;  
use warnings;  
my %H_list;  

open my $H_list, '<', 'listH.txt' or die "Cannot open listH.txt: $!"; 
+ 
while (my $line = <$H_list>) { 
    chomp $line; 
    $line =~ s/\r//g; # removes windows CR characters 
    $line =~ s/\s+$//; # removes trailing white spaces 
    $H_list{$line} = 1 
}  
close $H_list;  

my ($L_count, $H_count); 
open my $L_list, '<', 'listL.txt' or die "Cannot open listL.txt: $!"; 
+ 
while (<$L_list>) {  
    chomp;  
    s/\r//; 
    s/\s+$//; 
    $L_count ++; 
    print;
    if (exists $H_list{$_}) {
        $H_count ++;
        print ' On List H';
    }
    print "\n";  
} 

print "List L UNIQUES: $L_count; FLAGGED From List H: $H_count \n";
[download]

UPDATE: See for example node 776720.