Referee did not fully understand accepted paper I just got a paper accepted without revisions in a prestigious journal. This is of course nice. Reading the referee report makes me a bit worried, though. It is clear that the referee has gotten the basic ideas of the paper, and has identified what we also think is the primary contribution. It is, however, also clear that quite a lot of details regarding the implications of the primary result, were not correctly understood by the referee. 

What actions should I take from here? I of course want the paper published, but I am worried that people in general will misunderstand the parts about implications. Should I contact the editor and ask for another reviewer? Should I ask permission to re-write that part of the paper? Or should I just shut up and be happy to be accepted without revisions?
As is the custom on this site (or at least it should be) let's assume the premises of the question are correct - that is that it is indeed a prestigious journal.

Do nothing. 

In fact no: celebrate acceptance in the way you find most appropriate.

The fact that some people misunderstand what you're trying to say is not a basis to act after acceptance. It might indicate that you presented your results in a not so clear manner — which would speak in favor of refining your writing for future articles — but that would not be an exception in the scientific literature. At any rate, edits (other than very minor ones such as typos) after final acceptance are generally not allowed.

If you see errors in your article that are not trivial and you feel need addressing, the appropriate way to handle this is to publish an erratum. I imagine most journals have a standard procedure for that.