Contradiction with Matthew 28:10
Jesus instructs his disciples to go to Galilee, but in Luke 24:13, the event occurs near Jerusalem, not Galilee.
Matthew 28:10: Then said Jesus unto them, Be not afraid: go tell my brethren that they go into Galilee, and there shall they see me.
Contradiction with Acts 1:4
Jesus tells the disciples not to leave Jerusalem, contradicting the idea in Luke 24:13 that they are leaving Jerusalem.
Acts 1:4: And, being assembled together with [them], commanded them that they should not depart from Jerusalem, but wait for the promise of the Father, which, [saith he], ye have heard of me. [being...: or, eating together]
Contradiction with Mark 16:7
The angel tells the women that the disciples are to meet Jesus in Galilee, which is geographically inconsistent with Luke 24:13 where the event happens near Jerusalem.
Mark 16:7: But go your way, tell his disciples and Peter that he goeth before you into Galilee: there shall ye see him, as he said unto you.