The criterion of coherence, as it is traditionally understood, judges as authentic those elements which fit well with what has been established about Jesus by the other criteria. Yet, such a task will inevitably involve subjective analysis: what exactly constitutes coherence? Morna Hooker writes:
“Subjectivity is still a danger when we turn to the principle of coherence or consistency… We may be able to sort out what seems coherent (or incoherent) to us―but we are living in a completely different world, and what seems incoherent to us may have seemed coherent in first-century Palestine―and vice versa. Moreover, some of Jesus’ sayings―if they are genuine―are paradoxical, and that alone should perhaps warn us against looking for what seems to be consistent.”In fact, many have pointed out that the criteria are not typically consistent in the use of these criteria.
For example, there appear to be inconsistencies within John Meier’s analysis. Despite his call for objectivity, at points Meier denies the authenticity of various traditions despite recognizing that they meet the standards of his criteria. For example, Meier states that Matthew has to “strain” to explain how Jesus came to be associated with Nazareth. According to Matthew, Joseph went there because Archelaus, the son of Herod, was ruling Judea. Meier thinks this is a poor explanation since by moving to Nazareth Joseph was relocating to the territory of another son of Herod, Herod Antipas, who killed John the Baptist. Yet, as Dennis Ingolfsland points out, what Meier fails to mention is that Herod Antipas had yet to behead John. Moreover, fear of Archelaus was probably justified since Josephus reports that he killed three thousand Jews in Jerusalem after Herod’s death (cf. Ant. 17:218). 
Moreover, since the criterion is largely deeependent on the findings of the other criteria it is very likely that it will perpetuate and even magnify the problems created by them. Thus Ben Meyer wrote: “Any errors in the results obtained by the ‘dissimilarity’ principle are liable to be magnified by the principle of ‘coherence.’”
Furthermore, the criterion begs a fundamental question: why must we assume Jesus’ teaching never included elements that were on some level contradictory?
(In an upcoming post, I will discuss how Brant Pitre has redefined this criterion).
 Perrin’s definition is often-cited. See Perrin, Rediscovering the Teaching of Jesus, 43: “Material from the earliest strata of the tradition may be accepted as authentic if it can be shown to cohere with material established as authentic by means of the criterion of dissimilarity.” In particular, the criterion was developed by those doing parable research. See Dodd, The Parables of the Kingdom, 1; Jeremias, The Parables of Jesus, 11; Perrin, Rediscovering the Teaching of Jesus, 20-22.
 See Hooker, “On Using the Wrong Tool,” 577.
 Dennis Ingolfsland [“The Historical Jesus According to John Meier and N. T. Wright,” in Bibliotheca sacra 155 (20) 460-73] points out a couple of examples in the work of John P. Meier.  Meyer, Critical Realism, 137. See also Hooker, “On Using the Wrong Tool,” 577: “If the core material upon which we build our reconstruction of the teaching of Jesus is inaccurate, then the addition of material which seems to be consistent with that core is likely to reflect those same inaccuracies.” Similarly, see Stein, “The ‘Criteria’ for Authenticity,” 251.
 This point is emphasized by Jack T. Sanders, “The Criterion of Coherence and the Randomness of Charisma: Poring Through Some Aporias in the Jesus Tradition,” 1-25, who concludes that Jesus must have in some way have taught things that were at some level contradictory: “Understanding that Jesus was a charismatic leader of [a New Religious Movement] and seeing that, as such, he apparently employed randomness to increase his charisma, we must now give up the academic criterion of coherence… and recognize that Jesus said contradictory things” (24).