Contradiction with Matthew 13:58
Luke 4:31 states Jesus taught with authority in Capernaum, while Matthew 13:58 indicates a lack of mighty works due to unbelief in a nearby town.
Matthew 13:58: And he did not many mighty works there because of their unbelief.
Contradiction with Mark 6:5
Luke 4:31 speaks of Jesus teaching effectively, yet Mark 6:5 notes limitations in His ability to perform miracles in His hometown.
Mark 6:5: And he could there do no mighty work, save that he laid his hands upon a few sick folk, and healed [them].
Contradiction with John 7:5
Luke 4:31 describes Jesus teaching with authority, whereas John 7:5 mentions His own brothers did not believe in Him.
John 7:5: For neither did his brethren believe in him.
Contradiction with Matthew 11:23
Luke 4:31 shows Jesus in Capernaum, but Matthew 11:23 predicts its downfall for not repenting despite His mighty works.
Matthew 11:23: And thou, Capernaum, which art exalted unto heaven, shalt be brought down to hell: for if the mighty works, which have been done in thee, had been done in Sodom, it would have remained until this day.
Contradiction with Luke 4:24
Contradicts Luke 4:31 where Jesus is accepted in Capernaum, while earlier in the same chapter He points out a prophet is not accepted in His own country.
Luke 4:24: And he said, Verily I say unto you, No prophet is accepted in his own country.