Examples of Confidential Information in Real Estate?

The property manager may not give out personal information, such as Social Security Number, birth date, and any and all information which may lead to identity theft.
and any credit history he has obtained from a 3rd party source such as a Credit Bureau, credit card numbers and account numbers, and credit ratings.

How much a renter is paying and if they pay on time should only be revealed in cases where you have to do so- not casually. How well they keep their place would be also private from other renters since it is none of anyones business. If someone receives help from charity then you should not broadcast that. If the owner is thinking of selling the property you may be asked to keep that private and you should as part of your job.