Contradiction with 1 Corinthians 15:5
Luke 24:23 claims they saw visions of angels saying Jesus was alive, while 1 Corinthians 15:5 states Jesus physically appeared to Cephas and then to the twelve.
1 Corinthians 15:5: And that he was seen of Cephas, then of the twelve:
Contradiction with Mark 16:14
Luke 24:23 mentions an angelic vision, but Mark 16:14 describes Jesus himself appearing to the eleven as they sat at meat.
Mark 16:14: Afterward he appeared unto the eleven as they sat at meat, and upbraided them with their unbelief and hardness of heart, because they believed not them which had seen him after he was risen. [at meat: or, together]
Contradiction with John 20:19
Luke 24:23 reports a vision of angels, whereas John 20:19 describes the physical appearance of Jesus to the disciples.
John 20:19: Then the same day at evening, being the first [day] of the week, when the doors were shut where the disciples were assembled for fear of the Jews, came Jesus and stood in the midst, and saith unto them, Peace [be] unto you.
Contradiction with Matthew 28:9
Luke 24:23 says the women saw a vision of angels, but Matthew 28:9 states the women met Jesus in person as they were leaving the tomb.
Matthew 28:9: And as they went to tell his disciples, behold, Jesus met them, saying, All hail. And they came and held him by the feet, and worshipped him.
Contradiction with Acts 1:3
Luke 24:23 refers to an angelic vision, contrasting with Acts 1:3 which declares Jesus showed himself alive by many infallible proofs.
Acts 1:3: To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God: