Caroline Kennedy stopped angling for Hillary Clinton's vacant Senate seat in New York because of a "tax problem" and "potential nanny issue," according to a source close to Governor Paterson. I don't know if it's true, but if it is, she clearly is not qualified to take office as an appointed senator from the great state of New York.
However, she is definitely qualified to serve as Secretary of the Treasury. As long as she says she's sorry and claims that it was all just an incompetent mistake. Honest and complete tax returns not necessary.