Depends on what you mean by "Washington." A lot of politicians and reporters didn't have a clue what was going on. Some of those who thought they did, didn't know names and details. And people could keep different and conflicting ideas in their mind at the same time so long as they didn't have any definite evidence, so some who sort of "knew" about Jack's sex life didn't really "know."
It was well known in D.C. that Cord’s wife was JFK’s mistress. It was no secret.
The reporters knew exactly who she was, what she was. People who were in D.C. at the the time, everybody in the media, everybody on the Hill, it was known who she was, it was unspoken who did it.