According to Article 1, Section 6 of the US Constitution, “No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States which shall have been created, or the Emoluments whereof shall have been increased during such time.”
That means that no member of Congress who voted to increase the salary of an appointed position can be appointed to that position.  Congress (and Senator Clinton) voted recently to increase the salary of the Secretary of State from$186,600 to $191,300.  Therefore, Hillary’s out, right?
Not necessarily…from the NYT Caucus blog:

In the past, Congress has gotten around this by passing a resolution cutting the salary for the office at stake back to what it was before the nominee’s most recent election… This became known as the “Saxbe fix,” after it was used to facilitate President Richard M. Nixon’s appointment of Senator William Saxbe of Ohio as attorney general.

So this has been dealt with before, and it probably will be again.  But it’s an interesting quandary for the new Obama cabinet to have to deal with…