I am a Q skeptic, but for perhaps different reasons than others. When it really started for me was in Seminary. I was taking a synoptic gospels course and reading through various treatments of the synoptic problem. The 2/4 source hypothesis made a great deal of sense. On the surface, the arguments that Matthew and Luke were independent of one another seem strong. Surely, why would Matthew or Luke remove so much material from the other gospel had they been aware of it. So, in jumps Q, a common source, used by both but in different way. Great hypothesis. But, where this turned sour for me was the, dare I say, hubris involved in treating Q no longer as a hypothesis but as a fact. Q works as a hypothesis, but it is not an historical document. We have no copies of Q. Therefore, I was turned off by the treatments of Q which accepted it as a fact and not as a hypothesis. The fact that the critical edition of Q is 10 times bigger than the NA 27 Greek NT just caused me to get very frustrated at the Q scholarship. Other trends, such as finding three redactional layers in a hypothetical document of which we have no copies smacked of arrogance and hubris of the highest degree. Hence, my initial frustration with the direction of Q scholarship.
This frustration led me to seek other solutions to the synoptic problem and I stumbled upon E. P. Sanders and Margaret Davies Studying the Synoptic Gospels in which the authors point out places where the 2/4 source hypothesis is weak and demonstrate that arguments that Luke may have used Matthew are actually stronger than once supposed. Therefore, while not outright endorsing the Farrer hypothesis, Sanders and Davies certainly showed that there are alternatives to Q.
Finally, a simpler solution to the Synoptic problem. Markan priority has been firmly established, at least in my mind. The arguments are so strong for Markan priority that Griesbach just isn't a viable solution, though the simplicity is there. So, here, with the Farrer hypothesis, we have the best of both worlds: Markan Priority and a simple and elegant solution to the synoptic problem without the complications, and consequent hubris, of Q proponents. Simple: Mark comes first, Matthew copies Mark, and Luke copies and edits both Mark and Matthew. No need for Q.
But, while simple and elegant are nice, they are no guarantee of truth. I had to search further to find how strong the Farrer hypothesis might be. This of course led me to Mark Goodacre's the Case against Q. This is one of the best books I have read in the field in many years. Goodacre makes a compelling case that first, Markan priority is a must, but also that Luke could certainly have produced his gospel by copying the "Luke pleasing" elements in both Mark and Matthew. Goodacre shows many places where Luke may have edited Matthew in ways that previous scholars thought were not possible. I have not looked at the book in a while, but I think what sealed the deal for me is where Goodacre demonstrated what Luke did with the parable chapter in Mark 4. Essentially, Luke split up the long parable chapter. He used almost all of Mark's material but spread its contents throughout his gospel and did not keep Mark's material all in one place. This tendency of Luke then becomes a template for what Luke may have done with Matthew's Sermon on the Mount. This has for a long time been used as the best argument for why Luke could not have known Matthew: why would Luke tear up such a beautiful 3 chapter sermon written by Matthew. Yet, using Goodacre's demonstration of what Luke did to Mark's long discourse, one can see that Luke may have done the same thing with Matthew's Sermon. Luke keeps nearly all of the material from Matthew's 3 chapter sermon, but he splits it up. He creates a much shorter Sermon on the plain, using the beginning and ending of Matthew's Sermon on the mount, but he takes the middle portion of the sermon and spreads that material through the rest of the gospel. Certainly a possibility. I think it all the more likely given that Luke's reorganization of Matthew's material makes sense.
The Sermon on the Mount, as a sermon, is kind of a mess. It starts and ends well, but the middle seems muddled. Even modern commentators cannot agree on any sort of organization of chapters 6 and 7 of Matthew. In short, the sermon becomes a collection of seemingly disconnected sayings. All of the sayings in and of themselves are wonderful (which is why Luke kept them), but they certainly don't hold together. Luke's Sermon on the plain, however, is very well organized. It is easy to plot out the thought development and the thematic unity of Luke's Sermon. Then Luke takes the sayings of the Sermon on the Mount that seemed to be floating in space and relocates them to various places in his narrative where they make sense. This accomplishes 2 goals for Luke. One, it breaks up a 3 chapter interruption to his narrative, and two, it relocates marvelous sayings of Jesus from floating in the aether to concrete locations connected to his narrative.
In short, I am a Q skeptic first because of the hubris involved in treating Q as an historical document and not as a hypothetical document, and second because I believe that the Farrer hypothesis solves the synoptic problem not only with more simplicity and elegance than the 2/4 source hypothesis, but does so with a level of possibility or even probability than was previously thought to be the case.