Contradiction with Proverbs 28:9
While Psalms 54:1 emphasizes calling upon God for salvation, Proverbs 28:9 suggests that prayers can be detestable if one turns away from following the law.
Proverbs 28:9: He that turneth away his ear from hearing the law, even his prayer [shall be] abomination.
Contradiction with Proverbs 21:27
Psalms 54:1 calls for deliverance by God's name, however, Proverbs 21:27 suggests that the sacrifices (or appeals) of the wicked are an abomination.
Proverbs 21:27: The sacrifice of the wicked [is] abomination: how much more, [when] he bringeth it with a wicked mind? [with...: Heb. in wickedness?]
Contradiction with Isaiah 59:2
Psalms 54:1 suggests God responds to prayers for help, whereas Isaiah 59:2 indicates that sin can separate people from hearing God.
Isaiah 59:2: But your iniquities have separated between you and your God, and your sins have hid [his] face from you, that he will not hear. [have hid: or, have made him hide]
Contradiction with James 4:3
Psalms 54:1 calls to God for salvation, but James 4:3 notes that wrong motives can prevent prayers from being answered.
James 4:3: Ye ask, and receive not, because ye ask amiss, that ye may consume [it] upon your lusts. [lusts: or, pleasures]
Contradiction with Psalm 66:18
Contrasting Psalms 54:1, where God is asked to hear prayer, Psalm 66:18 implies that harboring sin can result in God not listening to prayer.
Psalm 66:18: If I regard iniquity in my heart, the Lord will not hear [me]: