Contradiction with Proverbs 27:2
Proverbs 27:2 advises to let others praise you instead of boasting about oneself, whereas Psalms 66:16 involves speaking of personal experiences with God.
Proverbs 27:2: Let another man praise thee, and not thine own mouth; a stranger, and not thine own lips.
Contradiction with Matthew 6:1
Jesus teaches against performing acts of righteousness publicly to be seen by others, while Psalms 66:16 involves publicly declaring what God has done for one's soul.
Matthew 6:1: Take heed that ye do not your alms before men, to be seen of them: otherwise ye have no reward of your Father which is in heaven. [alms: or, righteousness] [of your: or, with your]
Contradiction with Matthew 6:6
Jesus instructs to pray in private, yet Psalms 66:16 involves openly discussing God's deeds.
Matthew 6:6: But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
Contradiction with Matthew 7:6
Advises against sharing what is sacred with those who may not appreciate it, in contrast to the openness of sharing God's works in Psalms 66:16.
Matthew 7:6: Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.