560SEL faint clunking

When I apply my brakes at very low speeds on my 86 560SEL it feels like something "moves" in the rear of the car. Best description would be the way the car would feel if a rim was not tightened fully. Also, I feel a clunk going from drive to reverse and vice versa. In addition, when driving around 30 MPH, upon pressing the accelerator causing the car to downshift, feel a clunk coming from the rear of the car. My mechanic says this is caused from play in the rear end. Does this sound like a proper diagnosis. If not what else should be looked at? Thanks