As a family lawyer who has never had to address this particular situation:
Marriage, like contracts generally, requires legal capacity. Interestingly, the capacity required for marriage is generally figured to meet a lower standard than for other contracts; one can be too crazy or too stupid to validly buy a car and still get married.
An old generality is that the law requires compliance with licensure requirements, legal capacity for both parties, and solemnization, but that courts will be loose with these requirements, often finding that two out of three is sufficient. A rare instance of a film which deals with this issue accurately is the Alfred Hitchcock comedy Mr. and Mrs. Smith. There it is found that some technical problem existed with the procedure which was followed when Carole Landis and Robert Montgomery were married (they were on the wrong side of a county line or somesuch), but it is acknowledged that as they acted in good faith and have been living as man and wife for years, it really doesn’t matter.
If a person was so incapacitated by liquor that it wouldn’t be fair to hold them accountable for entering into the marriage, the marriage would likely be viewed as annullable, as distinct from actually being a nullity. That is, if the person acted promptly to have the marriage annulled they would likely succeed. If he or she were slow in taking action, or chose to act as though they were married for a while, the opportunity for annulment would likely be seen as having been foregone, and divorce would be the appropriate option. The court would likely hold that the party had ratified the marriage by their action or inaction.