when two baptized people are married by a notary public (legal in our state)…and the notary is a Eucharistic Minister (extraordinary)…what is the state of their marriage? 
Can they be remarried in the Church or is that necessary?
Dear jen,
For two non-Catholics the marriage is valid. If they are Catholics the marriage is not valid. After being married outside the Catholic Church, if neither of them have been previously married, two Catholics must be married in the Church before receiving Holy Communion. They will need to go to Confession as well. Whether or not the notary is an extraordinary minister of the Eucharist is irrelevant.
Fr. Vincent Serpa, O.P.