So here's the interesting thought: If Obama named Bill Clinton to his Cabinet, would Clinton be eligible to become President under the terms of the Presidential Succession Act? Answer: Yes, he would. Clinton is prohibited by the 22nd Amendment from being elected President a third time, but that doesn't prevent him from assuming the office should be be called upon to do so. He just couldn't run for election at the end of his term as Acting President.
And yes, I'm aware that I some of the things I find interesting are not. Deal with it.