Upon inspection, all of his marriages seem to be invalid:
Newt was not baptised until 1970 or 1971; his first marriage in 1962 was therefore not a Christian marriage at all.
In view of the fact that his first marriage was a civil marriage and not a sacramental one, the issue moves to his second marriage, which occurred after his baptism. If Marianne Ginther was indeed baptised as well, the case could be made that this marriage was indeed valid, but that would hinge upon the state of mind of the two at that time, which, given the likelihood that the marriage was based on Gingrich’s prior infidelity and the sterility of the marriage, very well may have not been congruent with the Church’s understanding of consent to marriage.
So then wouldn't a marriage that happened after '71 be Christian and therefore valid?