If we go with the assumption that an element never occurs more than once in a single array, we don't need to track the arrays seperately, and can use Perl's array flattening:

my %present;
for my $a ( @array1, @array2, @array3 ) { $present{ $a }++ }
my @only_two = grep $present{ $_ } == 2, keys %present;
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If we have to deal with multiples in any of the arrays:

use List::MoreUtils qw(uniq);
my %present = ();
for my $a ( uniq(@array1), uniq(@array2), uniq(@array3) ) { $present{ 
+$a }++ }
my @only_two = grep $present{ $_ } == 2, keys %present;
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my @array1 = (1,2,2); # 2 would be in the final array
my @array2 = (1);
my @array3 = (1);
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Modifying Fletch answer a little:

my @array1 =( 1, 3, 6, 8);
my @array2 =( 1, 2, 3, 4, 4);
my @array3 =( 1, 2, 3, 5, 6);

my %present;
my @arrays = ( \@array1, \@array2, \@array3);
for my $i ( 0 ..  @arrays - 1) {
    $present{ $_  }{ $i } = 1 for @{ $arrays[ $i ]  };
}

my @only_two = grep { 2 ==  scalar keys %{$present{ $_ }}  } keys %pre
+sent;

print "@only_two\n";
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OK, then how about removing duplicates before you check the arrays?