Does the Qur'an itself claim that the order of righteousness prescribed by it is absolutely faultless ?

Yes. It itself claims that it is the book which guides people onto the path of exemplary conduct.

'Verily this Qur'an doth guide to that which is most right (or stable).' (H.Q. 17:9)

The Qur'an is the last religious scripture that has been revealed to mankind. Indeed, the Qur'an constitutes the criterion to judge between truth and falsehood for all up to the very last man.

'Ramadhan is the (month) in which was sent down the Qur'an, as a guide to mankind, also clear (signs) for guidance and judgement (between right and wrong).' (H.Q. 2:185)

The Qur'an sternly reprimands those who  strive to acquire worldly comforts and pleasures like greedy animals. A reprimand that commands against the purchase of the affliction in the eternal life hereafter in exchange for the comforts of the world; a reprimand that reminds one of the perishable nature of the life of this world; that all the joys and sorrows herein are but temporary in their existence. The Qur'an further claims that it itself is the book of guidance for those who hasten to give ear to this divine warning and to accept the divine commandments.

To those who fail to understand that the progress of human society has in the ordering of life within the framework of morality, the commandments of the Qur'an will not, in any way, appear to be relevant. But for those who profess that the true realization of life lies actually in the ennobling of it, each one of the legal prescriptions of the Qur'an are invaluable; they realize that not one of these prescriptions can ever be the subject, or cause, of ridicule and mockery. To them the Qur'an constitutes the highest guide-book in all respects. Indeed, this has also been the contention of the Qur'an itself: 'This is the Book; in it is guidance sure, without doubt, to those who fear God.' (H.Q. 2:2)