Your for loop is giving testing everything after @dna[4], not every third one, as the $i is only being incremented by one each time through the loop. i.e.
Wasn't sure how to explain but here are the values of $i and $i + 3 each time through the loop:

$i $i+3
1 4
2 5
3 6

,etc...

I think what you are looking for is something more along these lines (as a for loop):

for ( my $i = 2; $i < @dna; $i = $i+3 )
{
  print "$dna[$i] at position $i\n";
  if ( $dna[$i]  eq 'C' or $dna[$i] eq 'G')
  {
   $counter++;
  }
}
[download]

Here the $i is incremented by three every time through the loop, which I believe is what you wanted.

-enlil