Writing on the Historical Reliability of the Gospels in Dictionary of Jesus and the Gospels (IVP), Craig Blomberg discusses seven areas of apparent disagreement between the Synoptic Gospels (Matthew, Mark and Luke).  For each, Blomberg indicates how the apparent difficulty might be resolved:-

(1) The theologies of the Evangelists may seem to conflict. Mark portrays the disciples as without understanding following Jesus’ walking on the water (Mk 6:52); Matthew has them worship him as the Son of God (Mt 14:33). In Mark, after stilling the storm, Jesus berates the disciples for their lack of faith (Mk 4:40); in Matthew he concedes that they have “a little faith” (Mt 8:26). Both tendencies are credible in light of the disciples’ mixture of faith and disbelief else where and each fits into distinctive emphases of the Gospels in which they appear.

(2) One Evangelist may seem to correct his source. In Mark, Jesus’ reply to the so-called rich young ruler seems to deny his goodness (Mk 10:18); Matthew rewords the comment so that Jesus merely inquires, “Why do you ask me about the good?” (Mt 19:17). Matthew is not contradicting Mark but trying to avoid a misinterpretation of him. Similarly, Luke reports Jesus as telling his followers to hate their parents (Lk 14:26); Matthew explains that this means they must love God much more than family (Mt 10:37).

(3) Events may appear in contradictory orders in different Gospels. Luke places Jesus’ rejection in Nazareth at the beginning of his Galilean ministry (Lk 4:16–30); Mark locates it much later (Mk 6:1–6). Usually, it is best not to assume chronology unless it is explicitly indicated. Luke has topically relocated this story at the front of his Gospel to show the type of rejection Jesus would receive from his native people throughout his ministry. In the same way, Luke reverses the order of the second and third temptations of Christ to build toward a climax with Jesus in the Temple in Jerusalem (Lk 4:1–13; cf. Mt 4:1–11). Both of these are key themes throughout his work.

(4) A passage may be so abbreviated that it seems to contradict a fuller parallel. Mark has Jairus and his companions come to Jesus twice, once to tell him of his daughter’s illness and once to say that she has died (Mk 5:21–43). Matthew so compresses the account that Jairus comes only once and tells Jesus right at the outset of the story that his daughter is dead (Mt 9:18–26). This type of literary abridgment was common in antiquity and not perceived as misleading or in error (cf. Lucian, How to Write History, 56). Similar telescoping appears in Matthew’s account of the withered fig tree (Mt 21:18–22; cf. Mk 11:12–14, 20–21) and in Luke’s account of Jesus’ trial before the Sanhedrin, if Luke is not in fact using a different tradition altogether, rather than Mark (Lk 22:66–71; cf. Mk 14:53–15:1).

(5) Sayings of Jesus may appear in different contexts. The Sermon on the Mount (Mt 5–7) and the Olivet Discourse (Mt 24–25) gather together teachings which are scattered all around the Gospel of Luke. Some of these may simply reflect Jesus’ repeated utterances; others no doubt reflect the common practice of creating composite speeches. Again, no one questioned the integrity of ancient historians when they utilized a device that modern readers often find artificial. Yet again, both sermons may be excerpts of a much longer original.

(6) A unique event may be told twice in apparently contradictory ways. Many see the feedings of the 5,000 and the 4,000 (Mk 6:32–44; 8:1–10) or the two anointings of Jesus (Lk 7:36–50; Mk 14:3–9) as doublets of the same events. In each case, these are probably better viewed as separate incidents.

(7) Names and numbers may appear to contradict each other. In Matthew Jesus heals two blind men along the Jericho road (Mt 20:30); in Mark he heals one (Mk 10:46). The latter does not exclude the former. In Mark Jesus exorcises a demoniac in the region near Gerasa (Mk 5:1); in Matthew it occurs in Gadara (Mt 8:28). The former is probably a city; the latter, a province.