Does the Stone of Jordan have any special properties or significance in Diablo 3?

Solution 1:

No, not any that is known at this time.

Solution 2:

With the expansion Reaper of Souls. Stone of Jordan has a guaranteed chance to roll

Increases damage against elites by 25–30%

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One of 7 Magic Properties (varies)

Physical skills deal 15–20% more damage.

Poison skills deal 15–20% more damage.

Lightning skills deal 15–20% more damage.

Cold skills deal 15–20% more damage.

Fire skills deal 15–20% more damage.

Arcane skills deal 15–20% more damage.

Holy skills deal 15–20% more damage.

This somewhat sets it apart from other rings. Other than that, it is just a ring.