D. A. Carson, writing on “Preaching the Gospels” in the new book Preaching the New Testament, ed. Ian Paul and David Wenham (Downers Grove, IL: IVP Academic, 2013), p. 26, gives some guidance for what to do when preaching on “material that apparently clashes with what is found in other Gospels”:
First, read widely enough in the commentaries that you do not automatically gravitate to the first ‘solution’ you stumble across. Complex issues almost always admit several ways of approaching the problem.
Secondly, be prepared to offer a solution in terms of probabilities: for example, ‘Of the various solutions that have been put forward, perhaps the most credible is . . .’ – or something of that order. In other words, many problems in Gospel harmonization are not so much incapable of resolution, as prohibitive of reasonable certainty. It is not that there are no answers, but that there are too many possible answers and too little information to warrant a strong voice on any of them.
Thirdly, do not use up much sermon time dealing with such issues. You may have to do enough work on the problem that you are reasonably clear in your mind as to which solution is most plausible (or least implausible!), but that does not mean you necessarily have to drop all your information and reasoning into the minds of the members of the congregation. Most such questions are the sorts of things you can address adequately in thirty seconds. That you have done so will alert the handful of people in the congregation who are aware of the problem that you have done your homework, and if any of them are troubled (e.g. undergraduate students in biblical studies), they will then feel free to approach you afterward for further information and bibliography.
Fourthly, it is almost always wise in such discussions to avoid expressions that sound vaguely superior or self-promoting: for example, ‘Although most scholars think such-and-such, I have come to the conclusion that this-and-that.’
Fifthly, the only occasions when at least a little more time in the sermon should be devoted to one of these perceived problems occur when (1) the way you address the problem has a direct bearing on the theological message you find in the passage, or (2) the manner in which you handle the text, complete with both knowledge and humility, becomes important as a way of modelling what it means to bow before Scripture with godly integrity.
The best book I know of on the subject of gospel harmonization is now Vern Poythress’s Inerrancy and the Gospels: A God-Centered Approach to the Challenges of Harmonization (Wheaton, IL: Crossway, 2012), recently reviewed here by Craig Blomberg.