How to communicate achievements on the StackExchange network in an academic CV or job interview? I think contributions to StackExchange constitute a valuable thing for an academic to do. In many cases such contributions are directly related to the aims of an academic department: community engagement, building new knowledge, etc.
This is particularly clear for sites that directly align with a particular academic discipline (e.g.,  mathematics, statistics, psychology).

However, many people in academia have not heard of StackExchange. They often won't have heard about the reputation system. They may not be aware of the high quality content that often appears.

Thus, as an academic, how should you share your achievements on the StackExchange network in contexts where how your performance is evaluated has material consequences? (e.g., a CV, job interview, grant application context, promotion context)
I routinely mention my participation in cstheory as a moderator on grant applications (under Broader Impact). I also mention it as part of 'synergistic activities' in my NSF 2-page bio. 

For departmental review, I'd view this as external service.