The basis of the Euro is on a multi-state entity with closed books and little regulation. This basically means the liability of any single country can impact the whole of the EU and by extension the Euro. Until the EU makes a part of membership, approval oversight on all member country budgets, the stability of the Euro is a bit fractured. (Getting oversight is something the countries generally refuse on the non-incorrect grounds of state independence, but then why join a combined currency in the first place? UK got it sorta correct)

And for clarity, the reason I see the multi-state being an issue is, it is slow to act to resolve issues or expose issues, since resolving issues takes a combined intent and single states have little incentive to keep their books correct publicly (plenty of upside, little downside).

While I don't see the dollar being the world currency forever, I also don't see it needs to be.