Contradiction with James 1:13
God does not tempt anyone with evil, contrasting with God permitting Balaam to go with men who intend harm.
James 1:13: Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man: [evil: or, evils]
Contradiction with Numbers 22:12
Earlier, God clearly tells Balaam not to go, which contrasts with Him later saying Balaam can go.
Numbers 22:12: And God said unto Balaam, Thou shalt not go with them; thou shalt not curse the people: for they [are] blessed.
Contradiction with 1 Samuel 15:29
God is portrayed as unchanging, contrasting with changing His instruction to Balaam from "do not go" to "you can go."
1 Samuel 15:29: And also the Strength of Israel will not lie nor repent: for he [is] not a man, that he should repent. [Strength: or, Eternity, or, Victory]
Paradox #1
Numbers 22:20 might seem inconsistent because God initially tells Balaam not to go with Balak's messengers, but later tells him to go on the condition that he only speaks what God tells him. It appears to be a contradiction in God's instructions.