Contradiction with Mark 3:14
Mark 3:14 states that Jesus ordained twelve disciples to be apostles, whereas Luke 6:13 implies that Jesus called a larger group of disciples and then specifically chose twelve from them.
Mark 3:14: And he ordained twelve, that they should be with him, and that he might send them forth to preach,
Contradiction with Matthew 10:1-2
Matthew 10:1-2 mentions that Jesus gave authority to twelve disciples and named them apostles, while Luke 6:13 implies the appointment of apostles took place in a more selective process from among a larger group of disciples.
Matthew 10:1-2: And when he had called unto [him] his twelve disciples, he gave them power [against] unclean spirits, to cast them out, and to heal all manner of sickness and all manner of disease. [against: or, over]