An indiscretion is a thing you say or do that shows poor judgment, especially something people think you should not have done. It can be a secret told at a party, a rude joke in the wrong room, or a more serious slip that looks bad morally. English often uses the word as a soft cover: “a youthful indiscretion” means “they were young, and we are choosing to treat it as one mistake,” even when the act was not small. Newspapers like this softening. The word can also name the habit of not being discreet, but you will meet the “one unwise act or remark” sense at least as often. It is formal. Though actually, calling something an indiscretion already takes a side — it makes the act sound smaller and more forgivable than a crime or a betrayal.