Looks suspiciouly like a homework assignment to me, but as you've actually posted code, here goes...:)

The first two lines stuff the arrays with the individual letters - it's not obvious from your code whether this is initially the case or not.

The '%pairs' hash demonstrates one way of avoiding large numbers of 'if' statements.

my @dna = split("","ATCTGCG"); 
my @comp = split("","TCTGCAA"); 
my %pairs = qw(A T T A G C C G); 
foreach (0..$#dna) {
    my $d = $dna[$_];
    my $c = $comp[$_];
    print "$_: $d - $c is a mispair\n" unless ($pairs{$d}  eq $c);
}
[download]

Hope this helps.

Update ROFLMAO! Marvellous how so many people can come up with the same routine written so many ways in 5 minutes :) Go monks! :)