Contradiction with Mark 11:24
Luke 17:14 emphasizes physical action of going to show themselves, while Mark 11:24 emphasizes belief that one has already received what is prayed for.
Mark 11:24: Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive [them], and ye shall have [them].
Contradiction with James 2:26
Luke 17:14 shows obedience leading to healing, whereas James 2:26 suggests faith without works is dead, implying faith must accompany action.
James 2:26: For as the body without the spirit is dead, so faith without works is dead also. [spirit: or, breath]
Contradiction with John 9:6-7
In Luke 17:14, the lepers are healed as they went, while in John 9:6-7, healing occurs after the blind man follows Jesus' instructions.
John 9:6-7: When he had thus spoken, he spat on the ground, and made clay of the spittle, and he anointed the eyes of the blind man with the clay, [anointed...: or, spread the clay upon the eyes of the blind man]
Contradiction with Matthew 7:7
Luke 17:14 involves no direct asking; healing follows obedience, whereas Matthew 7:7 encourages asking to receive.
Matthew 7:7: Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you:
Contradiction with Matthew 10:8
Luke 17:14 depicts healing through following specific instructions, while Matthew 10:8 suggests healing is a freely given gift that should be passed on freely.
Matthew 10:8: Heal the sick, cleanse the lepers, raise the dead, cast out devils: freely ye have received, freely give.