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Here is an analysis of areas where Jesus is viewed as being in contradiction or conflict:

His Birth: Matthew describes the family fleeing to Egypt, where as Luke suggests they returned directly to Nazareth after fulfilling the Law in Jerusalem.
Genealogies: Matthew and Luke provide different, irreconcilable genealogies for Joseph.
The Crucifixion Time: Mark 15:25 states Jesus was crucified at the third hour, while John 19:14-15 indicates it was the sixth hour.

Jesus vs. The Old Testament (Mosaic Law)
In the Sermon on the Mount, Jesus often uses the formula "You have heard that it was said... But I tell you," which appears to contradict or raise the standard of the Law:
Sabbath Laws: Jesus healed on the Sabbath and allowed his disciples to pluck grain, contradicting strict interpretations of the prohibition against working on the Sabbath.
"Eye for an Eye": In Matthew 5:38–39, Jesus directly contradicts the Mosaic law of retribution, instructing followers to "turn the other cheek".
Divorce: Jesus allowed divorce only in cases of sexual immorality, which was stricter than the provisions in Deuteronomy 24:1-4.
Dietary Laws: Jesus declared all foods clean (Mark 7:19), overturning Levitical dietary restrictions.
Oaths: Jesus prohibited taking oaths (Matthew 5:33-37), whereas the Old Testament allowed them in God's name.