This is a comon problem with clutch type limited slip differentials. Most of the time you only hear the noise and feel the car jerk at low speed and when making a sharp turn. Most of the time the GM or Ford additive will take care of the problem.
A new Eaton Posi should have the clutches tight enough that there will be very little axle end play. If you have a lot of axle end play then you might have some damaged clutches. A Eaton Posi that is set up correctly should have about .005 to .010 axle end play, but factory set up clutches might have more.