From the Washington Post:
A subsequent sampling of opinion from professors of constitutional law, former White House lawyers and even a couple of federal judges reveals a simmering disagreement on whether a president who has already served two terms can be vice president. Some agree with the conclusion that the presidential term limit embedded in the Constitution bars someone such as Clinton from returning to the White House even in the No. 2 slot. Others, though, call that a misreading of the literal language of the law.
As the former president might say, it all depends on the meaning of the word “elected.” Under Article II of the Constitution, a person is “eligible to the Office of President” as long as he or she is a natural-born U.S. citizen, at least 35 years old and a resident of the United States for 14 years. The 12th Amendment says “no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President.”
Okay, so that means if you’re not eligible to be president, you’re not eligible to be vice president. Makes sense. What would be the point of electing a vice president who can’t succeed the president in case of death, incapacity or vacancy?
But then Congress and the states added the 22nd Amendment in 1951 to prevent anyone from following the example of Franklin D. Roosevelt, who won four terms. That’s where things get dicey. “No person shall be elected to the office of the President more than twice,” the 22nd Amendment says.
On its face, that seems to suggest that Clinton could be vice president because he is only barred from being elected president a third time, not from serving as president.