use Scalar::Util (); # as advised by [choroba]

my ($line, @arr);

open my $fh, "<$ARGV[0]"
    or die "failed to open file $ARGV[0] for reading: $!\n";

my @check_fields = (6, 7, 8);

my $line_counter = 0;

LINE:
while ($line = <$fh>) {

    $line_counter++;

    ### skip line if any of fields 6-8 are not numeric
    @arr = split /\s+/, $line;
    foreach my $i ( @check_fields ) {

        if ( ! Scalar::Util::looks_like_number($arr[$i - 1]) ) {

        # bad;this checks only for positive integers
        # (thanks Not_a_Number)
        #  if ($arr[$i - 1] !~ /^\d+$/) {

            print STDERR "line num $line_counter: " .
                         "1st problem field $arr[$i - 1]: " .
                         "field num $i: " .
                         "$line\n";
            next LINE;
        }
    }

    ### the rest of your code

}