Here's a first pass at cleaning up the main loop of your code. It's not tested, so don't trust it, but it ought to do exactly the same thing, faster.

The code is easier to read this way. So easy that I can see a BUG! (I left it in with a comment).

The program could be made even clearer and further optimized, but this is a start. For example you can replace all the print DAT $c; with $all .= $c; and, wait till the end to open the file for append, print DAT $all;, and close.

By the way, if you can, you should test this in a standalone program on your computer, not just on the web.

# 1. Only open/close the file once to append, instead of $maxid times.
# 2. Use temporary values.
# 3. Delete stuff you don't need immediately, not next time around loo
+p.
# 4. In this case, ($c) is same as (defined $c) (cosmetic).

open(DAT,">>data/parsed-all.txt");
for(my $i = 1; $i <= $maxid; $i++) {
  my $currid = changeID($i);
  my ($c1,$c2,$c3) = ($compare1{$currid}, $compare2{$currid}, $compare
+3{$currid});
  delete $compare1{$currid}, $compare2{$currid}, $compare3{$currid};
  next if( $c1 && $c2 && $c3 && $c1 ne $c2 && $c1 ne $c3 && $c2 ne $c3
+ );
  if( $c1 && !$c2 && !$c2 ) {
    print DAT $c1;
    next;
  }
  if( $c2 && !$c1 && !$c3 ) {
    print DAT $c2;
    next;
  }
  if( $c3 && !$c1 && !$c2 ) {
    print DAT $c2; # <-- BUG HERE!
    next;
  }
  if( $c1 && $c2 ) {
    if( $c1 eq $c2 ) {
      print DAT $c1;
      next;
    }
  }
  if( $c1 && $c3 ) {
    if( $c1 eq $c3 ) {
      print DAT $c1;
      next;
    }
  }
  if( $c2 && $c3 ) {
    if( $c2 eq $c3 ) {
      print DAT $c2;
      next;
    }
  }
}
close(DAT);
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