He has been criticized for showing 'indiscretion' in his remarks. [=for carelessly saying things that should not be said]
He describes his drug use in college as just a 'youthful indiscretion'. [=a minor mistake made by a young person]
She committed a few minor 'indiscretions'.
(..) I must warn you about something. Warn me? Oh, it's really rather late. I wish to warn you that you may, inadvertently by indiscretion and carelessness, give the world occasion to talk about you. I am not a committee. Please say what you want to tell me. You and Count Vronsky (..)2012 Anna Karenina