The most compelling contradictions are found by reading the synoptic gospels 'horizontally'. That is, read an account in Mark (the earliest gospel) then read the same story in Matthew and Luke.
It is impossible to reconcile Jesus' birth and death narratives.
Was Joseph and Mary living in Galilee and then went down to Judea and later returned to Galilee, or were they living in Judea and then later fled to Galilee?
On what day did Jesus die, the Passover or the day or preparation for the Passover?
At what time of day was Jesus impaled? (You will need to include John's gospel for this one)
Who went to the tomb and what did they see?
Did the resurrected Jesus meet his disciples in Judea or Galilee?