Contradiction with Matthew 28:9
In Matthew 28:9, Jesus personally appears to the women at the tomb, whereas Luke 24:22 suggests the women merely had a vision of angels.
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 John 20:14-17
John 20:14-17 details Mary Magdalene speaking directly with Jesus, contradicting Luke 24:22's implication of only witnessing angels.
John 20:14-17: And when she had thus said, she turned herself back, and saw Jesus standing, and knew not that it was Jesus.
Contradiction with Mark 16:9
In Mark 16:9, Jesus first appears to Mary Magdalene explicitly, in contrast to the mention of angels in Luke 24:22.
Mark 16:9: Now when [Jesus] was risen early the first [day] of the week, he appeared first to Mary Magdalene, out of whom he had cast seven devils.