Secrets could be twofold:
1) Related to the sim themselves and chosen by the player. That could be their occult type or things like "Is bribeable" for a detective. Each secret can get named whatever the player likes and must be tied to a characteristic. "I don't know what to write in here, I just want to play with the mechanic" is a legitimate secret.
Learning the secrets could be the objetive of a new private investigator career and if the secret become public the sims suffers a hit to the aspect the player has chosen.
Examples:
"Loves llamas a bit too much" - Aspect: Romance (Existing romantic relationships take a hit if exposed)
"Doesn't wash their feet" - Aspect: Career (Sim takes an instant hit to career performance if exposed, can lead to a demotion)
"Eats junkfood" - Aspect: Fitness skill (Fitness skill meter drops if exposed, cannot lead to loss of a skill point)
In this example sims that eat junkfood have no negative consequences, only the one sim that hides the fact that they do it takes the hit.
"Actually is wife writes all his songs" - Aspect: Fame (Sim's fame takes a hit, this requires Get Famous)
High-mischief sims could attach rumours to other sims that would work the same as secrets.
2) Secrets acquired during gameplay, for example when a sim has attempted hacking. If found out the sim with that secret has to pay a fine. These secrets should fade and become worthless after some time.