I'm wondering if the phrase "Who's who" as in "a who's who of the community" should be "Who's whom" on the basis that if you rephrase to a question and remove the apostrophe you get "Who is who?" which is poor English, so should be "Who is whom?" (since you would respond to it phrased as a question with, for example "He is him(self)".
Which is technically correct, "Who's who" or "Who's whom".
I'm pretty sure it should not be "Whose who" because that would be possessive. Ignore that who and whom are generally interchangeable in modern common usage, I want to be technically correct about it if possible, though I fear it may just be one of those statements which makes no sense but we use anyway.