$text was undefined at one point at which it was used, in sub main.

I think this fixes it. Replace:

my $romaji = plaque("@romaji");
    my $hiragana = plaque(hiragana($text));
[download]

With:

my $text = "@romaji";
    my $romaji = plaque($text);
    my $hiragana = plaque(hiragana($text));
[download]

Also, since you invited comments/criticisms, I would rewrite your "pick a few" section as:

Other useful resources: Unicode Code page for Hiragana which I used (and I assume you did, too), along with charnames to simplify your %Hiragana generation:

my %Hiragana;
use charnames qw/hiragana/;
sub get_hiragana { chr charnames::vianame("HIRAGANA LETTER ".uc(shift)
+) }

# the standards
for my $initial ('', qw/k g s z t d n m h b p m r/) {
    for my $final (qw/a i u e o/) {
        my $syl = $initial.$final;
        $Hiragana{$syl} = get_hiragana($syl);
    }
}

# columns with missing entries (yi, ye, wu)
$Hiragana{$_} = get_hiragana($_) for qw/ya yu yo wa wi we wo n/;

# small letters
$Hiragana{"($_)"} = get_hiragana("small $_") for qw/a i u e o ya yu yo
+/;

# special cases
{
    my @special = (qw/tsu tu shi si chi ti fu hu/,
                   map(('j'.$_ => 'z'.$_), qw/a i u e o/),
                   '(tsu)', 'small tu');
    while (my ($syl, $uni) = splice @special, 0, 2) {
        $Hiragana{$syl} = get_hiragana($uni);
    }
}
delete $Hiragana{$_} for qw/tu si ti/; # delete Unicode-y names for ts
+u, shi, and chi
[download]

Very cool use of Perl. Brings me back to my Nihongo days...