All nations would certainly benefit since there would no longer be currency risk in international trade. Traders would no longer fear for currency fluctuations.
If everyone is using the same currency, it would still change its value, because nothing can be stable on the free market, the whole point of free market is that prices change freely to reflect the objective value. Even if there's no other currency, this world currency will be benchmarked against common comoodities like oil or hamburgers.
Also, the USD is already a world currency, it's used for a large share of international trade and you can exchange it in every country in the world, and often can even pay with it outside of the USA.