Contradiction with Matthew 13:34-35
These verses mention Jesus speaking in parables to fulfill prophecy, suggesting not everything was plainly explained as Luke 24:27 implies.
Matthew 13:34-35: All these things spake Jesus unto the multitude in parables; and without a parable spake he not unto them:
Contradiction with John 16:25
Jesus indicates he has been speaking in figurative language, whereas Luke 24:27 suggests he explained things clearly.
John 16:25: These things have I spoken unto you in proverbs: but the time cometh, when I shall no more speak unto you in proverbs, but I shall shew you plainly of the Father. [proverbs: or, parables]
Contradiction with Mark 4:34
States that Jesus only explained things to his disciples privately, in contrast to Luke 24:27 implying a more public revelation.
Mark 4:34: But without a parable spake he not unto them: and when they were alone, he expounded all things to his disciples.
Contradiction with Isaiah 6:9-10
This prophecy speaks of people not understanding, which contradicts the clear understanding implied in Luke 24:27.
Isaiah 6:9-10: And he said, Go, and tell this people, Hear ye indeed, but understand not; and see ye indeed, but perceive not. [indeed, but understand: or, without ceasing, etc: Heb. in hearing, etc]