"nervous about" and "nervous of"

I would say that nervous about describes your anxiety towards the process and possible outcome of a situation, while nervous of describes a general apprehension or (well-founded) scepticism towards the situation itself and is almost a synonym of ‘leery’.

So if you’re nervous about an exam, your anxiety is aimed at the actual process of going through the exam, as well as what the outcome of the exam will be; while if you’re nervous of exams (a bit odd, though in no way an unthinkable phrasing), you are apprehensive of exams as a general thing, feeling that they are not a thing to be trusted.

Of course, being nervous about someone is not at all the same as being nervous of them. If you’re nervous about someone, you have their welfare in mind and you are worrying that something is bothering them (for example); whereas if you’re nervous of them, you are leery of them.

I agree that these two meanings can be quite hard to disentangle (and dictionaries strangely do not seem to mention the distinction at all). It also appears that nervous of is far more common in British English than in American English:

• The British National Corpus has 113 hits for nervous about and 78 for nervous of.
  Ratio: 0.69026549
• The Corpus of Contemporary American English has 1,402 hits for nervous about and only 6 (!) for nervous of.
  Ratio: 0.0042796006

That is definitely a statistically significant difference, one that I never consciously realised before.