The following contradictions are taken from the genealogies of Jesus as told in Matthew 1:1-17 and Luke 3:23-38.
WHO IS THE FATHER OF JOSEPH (NIV) Contradiction 1: And Jacob the father of Joseph, the husband of Mary, of whom was born Jesus... Matthew 1:16 (NIV) Contradiction 2: Jesus...was the son, so it was thought, of Joseph, the son of Heli. Luke 3:23
Though this belief is not unanimous, it is generally accepted among scholars that Matthew records the genealogy of Joseph while Luke records the genealogy of Mary. Jacob is believed to be the biological father of Joseph while Heli is believed to be the father of Mary and the father-in-law of Joseph. If Heli only fathered the two daughters mentioned in the New Testament it is possible Joseph, the son-in-law, would be mentioned as his son in order to preserve the family name and inheritance.
THE NUMBER OF ANCESTORS BETWEEN ABRAHAM AND JESUS Matthew directs his Gospel to a Jewish audience and records the genealogies from Abraham to demonstrate Jesus' Jewish heritage. Luke addresses his Gospel to a Gentile audience and records the genealogies to Adam to allow all of humanity to identify with their Savior. But why does Luke record more generations from Abraham to Jesus than Matthew? One possible solution, referred to as an open genealogy, is that Matthew paraphrased Jesus' ancestors in order to make the Gospel easily remembered for oral evangelism. This is evident when he organizes his genealogy into three sets of fourteen: 14 generations from Abraham, 14 generations from David, and 14 generations from the exile. Matthew also uses the word gennao which can refer to either an immediate or long-term descendant (as in a patriarch begetting his descendants, although not directly). On the other hand, Luke uses the word ho which represents the son of (definite article). Luke also recorded his Gospel using a more historical approach as compared to Matthew, Mark, and John (which explains his more thorough documentation).
THE CURSE OF JECONIAH (NIV) Contradiction 1: This is what the Lord says, "Record this man [Jeconiah] as if childless, a man who will not prosper in his lifetime, for none of his offspring will prosper, none will sit on the throne of David or rule anymore in Judah." Jeremiah 22:30 (NIV) Contradiction 2: Jeconiah was the father of Shealtiel... Matthew 1:12
Because Jeconiah is cursed to be childless and his descendants cannot inherit David's throne, why is he listed as Jesus' ancestor? First of all, Jeremiah does not state Jeconiah is childless but he will be recorded as if childless (a great insult in antiquity). Also, the curse does not appear to be permanent (will not prosper in his lifetime) as we can see God promises to raise up a righteous branch from David (but this would be impossible if David's line was just wiped out). Another theory is that this is not even the same Jeconiah, for the only thing the two seem to have in common is their name: both have different parents, different children, and are from different sons of David. One last possible explanation is if we assume the curse was eternal, technically Jesus was not even a blood descendant of Jeconiah. Jeconiah is mentioned in Joseph's genealogy but not Mary's. Because Matthew's genealogy is a lineage-via-adoption, we can assume Jesus is not even a blood relative of Jeconiah.
HUMAN OR SUPERNATURAL CONCEPTION (NIV) Contradiction 1: The patriarch David died and was buried... but he was a prophet and knew that God had promised him on oath that he would place one of his descendants on his throne. Acts:2:29-30 (NIV) Contradiction 2: [Jesus'] mother Mary was pledged to be married to Joseph, but before they came together, she was found to be with child through the Holy Spirit. Matthew 1:18
Both Luke and Matthew acknowledge the virgin birth in their genealogies: Matthew interjects Mary's name into Joseph's genealogy before mentioning Jesus' birth: Joseph, the husband of Mary, of whom [feminine] was born Jesus. Luke uses the wording He was the son of Joseph, or so it was thought as his disclaimer. When the Messiah was promised to be born from David's line, this was indeed fulfilled. Mary was the biological parent of Jesus and descendant of King David (which fulfills the promise to David literally) while Joseph was the adoptive father of Jesus and biological descendant of King David.