I believe there is but someone can probably confirm or deny it with more authority than I. It places him in direct succession to the presidency and that is not allowed. Surely you’re not worried about it are you?
-there is also the provision that both president and vp cannot be from the same state........oh, wait, you are speaking of the clintoons who don’t live together......
If the time came when Hillary is incapacitated and has to be replaced, then if the VP is not qualified, we go to the next in line, right?
Let's look at the next in line after the VP, the Speaker of the House of Representatives. That person doesn't have to be a native born American to hold that office yet they are in direct line of succession.
In other words, does a person have to qualify to be elected president in order to hold an office that is in direct line of succession? I don't think so.
Therefore, I conclude that the succession reason is not in play for disqualifying Bill.