De Nederlandsche Bank has reported on the security of debit-card payments and direct debits to the Ministry of Finance, that has reported to the Parliament (see this link). The main conclusion is that for now, there is no need to worry about security of these instruments.
The investigation followed after some fraud incidents with both instruments last year. It turns out that 800 debitcards were copied and 20 direct-debit frauds occured. DNB does one suggestion in its reports: to determine the product conditions for the use of the direct debit on the web. The solution to this issue has been proposed earlier on this weblog (see previous entry) and could be implemented quite quickly.