Contradiction with Acts 1:3
This verse explains that Jesus spent 40 days with his disciples after his resurrection, which contradicts the implication in Luke 24:28 that suggests Jesus intended to leave them earlier.
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:
Contradiction with Hebrews 13:5
This verse assures that God will never leave nor forsake us, which contradicts Luke 24:28 where Jesus acts as though he would leave the two disciples.
Hebrews 13:5: [Let your] conversation [be] without covetousness; [and be] content with such things as ye have: for he hath said, I will never leave thee, nor forsake thee.
Contradiction with Matthew 28:20
This verse promises that Jesus will be with the disciples always, contradicting the implication in Luke 24:28 that he would have continued on his way without their insistence.
Matthew 28:20: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, [even] unto the end of the world. Amen.