OK, let's get rid of that big hash, if you think that's where the trouble is:

WORD: while (<DATA>) {
  chomp;
  my $key = lc $_;
  my $signature = join "", sort split //, $key;
  my $list = $words{$signature} ||= [];
  lc $_ eq $key and next WORD for @$list;
  push @$list, $_;
}
for (sort keys %words) {
  my @list = sort @{$words{$_}};
  next unless @list > 1;
  print "@list\n";
}
__END__
Abby 
abbot 
acne 
alert 
alter 
baby 
Baby 
BABY 
best 
bets 
cane 
later 
Unix 
UNIX
[download]

How's that do?

-- Randal L. Schwartz, Perl hacker