Contradiction with Matthew 10:5-6
Jesus instructs his disciples not to go to the Gentiles or Samaritans, but only to the lost sheep of Israel, whereas in Mark 1:39, He preaches throughout all of Galilee, including Gentile regions.
Matthew 10:5-6: These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into [any] city of the Samaritans enter ye not:
Contradiction with John 4:9
The Jews typically did not associate with Samaritans, yet Jesus' actions in Mark 1:39 imply he was preaching broadly.
John 4:9: Then saith the woman of Samaria unto him, How is it that thou, being a Jew, askest drink of me, which am a woman of Samaria? for the Jews have no dealings with the Samaritans.