The most common symptoms of failure in differentials are noise and leakage. While they are often mistaken as the only problem, both are more often the symptom of another problem. For instance axle seal leakage often indicates a worn axle shaft, bad axle bearing or a plugged vent tube. In this picture oil can be seen on the backing plate on the left rear wheel.
Once the rear wheel, brake caliper and brake rotor are removed, the nature of the leak is easier to see. The rear parking brake shoes are also contaminated with oil and will have to be replaced.
Removing the axle shows the actual problem. This axle shaft is badly grooved and causing the leakage.
The right side is also leaking, to a lesser degree.
While bad axle seals allow oil to leak out, they can also allow water to leak in. This can be a far worse problem. The milky colored oil in this differential indicates water contamination.
The ring gear has been damaged by corrosion and is the source of noise in this differential.
Water also often enters a differential through a damaged vent tube. In this instance this is not the case as the vent tube is still fully intact. Driving though water, above the height of the axle can allow it to enter the differential.
Best is to avoid driving though high water and have leaking seals addressed immediately. Professionals like AGCO Automotive can spot and often prevent more serious damage. Properly servicing this differential might have prevented an expensive rebuild, replacing the ring and pinion gears. Avoiding repairs rather than simply repairing damage, that's the AGCO way.