my $q   = 'INSERT INTO some_table (data) VALUES (?)';
my $sth = $dbh->prepare($q);
{
    local $dbh->{RaiseError} = 1;
    while(my $data = $csv->get_next_line()) {
        eval{
            $sth->execute($data);
        }

        if($@) {
            next;
        }

        # More code here...
    }
}

##</code><code>##

while ( my $data = ... ) {
    $sth->execute( $data )
        or next;
}