I've been an external examiner now for three doctoral dissertations on Hebrews. This is a great honor and also a good way to keep your pulse on Hebrews' studies. It is also very interesting because I'm usually asked in relation to confessional communities that each have their own landmines and understood criteria that the candidates have to navigate.
For example, a doctoral student in a Seventh Day Adventist context has to navigate Ellen White. Someone in a strong evangelical community will navigate critical issues in a certain way. And someone from a conservative Reformed context might navigate issues of second repentance in a certain way.
But what are the key things I look for in a dissertation:
1. The most crucial thing that I am looking for is what you might call a "doctoral spark." This is ultimately the basis for the degree. Where in this dissertation has the candidate demonstrated that he or she can think originally and creatively in a super-competent way that advances the scholarly discussion and isn't just nuts?
2. Obviously we want a clear thesis that is tightly argued throughout the dissertation.
3. We want good organization. The introduction should set down the method followed and give necessary theoretical background on the scholarly discussion up to this point.
4. If I were the doctoral advisor, I would want clear hermeneutical distinctions. This is one area where as an external examiner I feel I need to respect the norms of the institution for which I am examining. For me, a dissertation should not be preachy, should not blur application with interpretation, should evidentiarily oriented (especially to the degree it is exegetical), and a host of other things that indicate hermeneutical competence to me.
5. It goes without saying that an exegetical dissertation should demonstrate thorough knowledge of the primary texts being investigated and the original languages associated with them. In the case of the New Testament, the text must be engaged in Greek, not in English.
6. The dissertation should demonstrate a thorough knowledge of the secondary literature relevant to the topic. This includes scholarship in German and French. It includes books and articles. Popular works should not be used.
In any case, there's a thumbnail sketch of what you should expect if you get a Ph.D.