[little jeremiah]

The courts will use "de facto officer" doctrine to allow most acts to have force, even though those acts have flawed authority underneath.

What if the non-eligibilty was proven to be a conscious criminal fraud?

[jjotto]

No difference. The De Facto Doctrine is meant only to prevent chaos, not to protect the innocent or even punish wrong-doers. Appointments and acts can be undone by conventional means and normal prosecutions can proceed, but government is going to continue uninterrupted.

[Cboldt]

-- What if the non-eligibilty was proven to be a conscious criminal fraud? --

Makes no difference. The rationale or basis for the doctrine is to minimize chaos. The doctrine is not always applied. There have been improvidently seated officials whose decisions were ditched, but that typically happens when the decisions affect a small number of people, like "one."

There would be considerable political and public pressure to remove Sotomayor and Kagan from SCOTUS, and perhaps other judges; but their participation in past cases would not cause all of those cases to fall out, and those judges would very unlikely do the honorable thing and resign.