If she wins, Bill would be expected to be a prominent first gentleman due to his former office, which could make for confusing headlines. A generation later she'll be one of two Former President Clintons. We know that Bill was reasonably popular (reelected, high approval ratings) so it'll be tough for her to be the first Clinton people think of, even with the significance of the milestone of first female President.
Sure, but currently, many journalists for example refer to "President Obama". If HRC becomes prez, surely they'll call her "President Clinton", no?
I can see the letter address:
The Presidents Clinton
1600 Pennsylvania Avenue
Washington, DC 20500
I assume "The Presidents Clinton" would be the proper form, just as you would write to "The Doctors Smith" or "The Professors Johnson" today. One could almost see a pseudo-monarchic distinction, "The President" being Hillary while "President Clinton" is Bill.