Probably upfront you should know that when the Discrete Opportunity Screen appears, you are being invited to partake in something illegal or unsavory.  By all means, these little silent opportunities can benefit you if no one finds out.  They could help you out with you health, money, promoting, and even state support.  It is very rewarding if you don't get caught.  Accepting or refusing a discrete opportunity is as simple as clicking Yes or No.

If you get caught, you'll know it immediately upon entering your response.  Getting busted can by far do the worst damage to you than any other situation in the game, even a Slander Article.  This is because you were caught red-handed in the middle of the act!  Damage can range from an unpopularity increase to losses in state support.

Is it recoverable?  It is... but you'll have to do some heavy kissing up to get through this one.