Application details can be be reviewed in a dedicated page accessible from the My Apps section. This is also where you can set the application as a public or private and as a reference application.
Before trying to switch an application to public or private, make sure you are granted the Edit Application right and are working work in the context of the company which owns the application (i.e., the company which released the application).
There is no more than one reference application for a given application type. If it is not possible to unset an application as the reference because the switch button is deactivated, set another application with the same type as the reference. This will automatically update the other.