What are the benefits of an oral exam? A recent question about reducing stress in oral examinations asserted that


  Oral exams can have various pedagogical benefits in certain circumstances


Based on the reputation of the poster I'm inclined to believe this, but what exactly are these benefits? As an engineer who has never had an oral examination in my academic career (excluding thesis and standard presentations), it's not clear to me what the benefits are. The only intuitive benefit I can think of is for courses where the oral aspect is inherent in the subject matter, such as foreign language or debate. Are there benefits that are more general and not directly tied to the subject? Are there subjects for which an oral exam is never appropriate?
Pedagogical advantages:


It is much easier to catch misunderstandings early and thus "rescue" an answer. After all, bad exam questions aren't that rare (bad as in: if the student has a very good understanding of the subject, they may be able to guess what topic the examiner has in mind).
Misconceptions can be corrected: while a written exam gives a snapshot of what the student understood or not, in an oral exam the examiner can ask the student to think again if the answer is wrong. Or can give a counterexample that takes into account the student's answer
In the end, an oral exam can be a discourse on a subject, which IMHO allows for better/easier grading. 
Related: the difficulty can be adjusted during the exam according to how much the student knows. 
Many oral exams I had had a "mixed" approach for deciding how deep into each subject to go: often 2 subjects were covered in depth (one by choice of the student, one by choice of the examiner) and a number of other topics touched. Particularly letting the student choose a subject of their liking (usually as the beginning of the exam) is not possible with written exams. 


Practical consideration:


if only few students are to be examined, oral exams take much less time for the examiner. 


Disadvantage:


If the examiner is somewhat off in estimating the difficulty of their questions, a written exam at least has the same questions for every student.