This is a variation on a faq -- see perlfaq 4, "How can I count the number of occurrences of a substring within a string?".
Using a little eval trickery :

foreach (<DATA>) {
    my ($w1, $w2) = split / /, $_;
    my %common = ();
    foreach ( split //, $w1){
        eval "\$foo=\$w2=~tr/$_/$_/" unless exists $common{$_};
        $common {$_}=1 if $foo;        
    }
    print "$w1 and $w2 have ", join (", ",sort keys %common)," in comm
+on\n";        
}
__DATA__
perl monk
help temp
frood hoopysdf 
bilbo baggins
jibber jabber
[download]

I wonder about your algorithm in score2, though. It seems to return 1 regardless of actual matches because of the last. Perhaps you need a larger/ more complex word set?