If he is "allowed" to serve out the entire term and "merely" be voted out or disqualified during the next round...his precedent will have been set. Future POTUS candidates who were born with foreign citizenship will now be eligible (WAY past the grandfather clause). It would follow, naturally, that Naturalized citizens will be promoted next.
And yes, states must have something in place going forward, so as to prevent this mess from happening in the first place. However, a requirement to show a B.C., does not answer the question of weather or not people born citizens of foreign countries are NBC’s of the U.S.