Contradiction with Matthew 6:1
Psalms 71:16 speaks of declaring God's strength, while Matthew 6:1 warns against practicing righteousness to be seen by others.
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 Proverbs 27:2
Psalms 71:16 involves proclaiming God's acts with one's voice, while Proverbs 27:2 advises letting others praise you, not your own mouth.
Proverbs 27:2: Let another man praise thee, and not thine own mouth; a stranger, and not thine own lips.