Q: Every wife in the village instantly knows when a man other than her husband has cheated but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. What happens?
A: Hilarity Ensues. (I love it when hilarity ensues)
Q: Every wife in the village instantly knows when a man...
If only one man is cheating, then every woman in the village knows that fact except for his wife. Since she knows at least one man is cheating and she doesn't know his name therefore the only man it could be is her husband. Stab.
If two husbands are cheating, every wife will know the name of one or two of them. The first night everyone is sure that some other husband will be killed. When none is (because the two cheated on wives already know one and only one name so don't kill their husbands), everyone will realize that not one but at least two husbands cheated. Those wives who only know of one husband who cheated realizes that their own husbands also cheated and kill them. Stab. Stab.
Extended, if X husbands cheat then they will be killed on day X, but not before because the victimized wives know of X-1 cheaters and will allow X-1 days to pass before they realize the number of cheaters exceed their known cheaters list.