I'll throw out some initial thoughts, but these are by no means recently researched concepts; instead, they are aggregations of things I seem to recall having read at some previous point - otherwise known as memory. Considering that my memory has been known to be faulty and/or inaccurate, my initial thoughts may be poisoned by that fact.
Also, I have purposefully avoided the `Who is following Wisconsin` thread (I've occasionally peaked, but never read through it) for various reasons; as such, I cannot be held responsible for recapitulating previous ideas/thoughts/posts.
Considering that it is helpful to know what words mean, I think I would first define what it is that I, personally, mean when I refer to a reserve currency (relative to what others may mean - others may have a more involved and expansive definition, or a more narrow and restricted one): the currency that the majority of the central banks around the world prefer (or are compelled, as the case may be) to purchase in order to form the bulk of their foreign exchange reserves.
Given that such a definition is fairly unitary (i.e. it implies that there is a single currency that is better than all other possibilities), it occurs to me that there will come a day where the U.S. dollar is no longer the preferred option (whether that is approaching now or not is debatable and outside the scope of the OP's inquiry). As such, to me, when that day arrives is not so much as a "what if" as a "when"; to the meat and potatoes of the question.
Given the state of international finance, (as I see it from my largely irrelevant perspective), I think that all wealthy institutions (which, for brevity in future paragraphs, I consider to include individuals) have an interest in finding the best opportunity for their money, regardless of the suffering, panic, or fiscal devastation it causes. If the dollar were to fall far enough out of favor with the powers that be (read: wealthy institutions), is there some patriotic reason they would try and artificially support the dollar? I would argue "no", and would advocate the position that they would move their money as discretely as possible before the reality became unavoidable.
Once reality set in (i.e. the public and the masses realized that the dollar no longer represented what it once did - guaranteed ROI, stability, etc), I think the middle class would probably evaporate into a higher and lower strata, and whether the majority landed in the higher or lower section would determine whether a violent revolution or a loud groan would occur - a brief description of what I think I mean can be found in a previous post I made here -
Outside the realm of what the masses would do (revolution vs non-revolution), I don't think the world at large would skip more than several beats. Central banks around the world would establish equilibrium elsewhere (presumably, at this point, the Euro or some other quasi-stable, plentiful, and manipulable currency), and would let the masses do what they may. From their point of view, what do they care what others do - as long as my wealth is worth what it was previously (or thereabouts, within reason), there is no difference; in my opinion, that is the beauty of currency baskets and exchange rates.
A particular example of the world not skipping but several beats can be found in the dissolution of the Soviet Union; yes, people were in awe and could barely believe it at first - then, after a month or so, people adjusted to the new power structure (i.e. a U.S.-centric model of the globe) and began to find new ways to exploit it for their own personal or organizational gain. Why would the collapse of the dollar be any different?
In conclusion, I would put forth yet another of my opinions, which is that the dollar is not inherently sacred or valuable, it is only a storage unit of perceived value; any other currency (be it cat poop, dog hair, or the euro) is equally capable of having value - which is the elegance (or danger, depending on your perspective) of a fiat currency.
The people who control/are employed in international finance get this, in my opinion. It's why they don't care whether the U.S. dollar is replaced or not; it's entirely irrelevant to them - they will simply bolster a new unit of value.
edit: I would clarify that the perceived unit of value of the dollar is global; that is to say, there is a single currency that is above all others at one point in time, and that there is no room for any others. An alternative would, by definition, not facilitate a global reserve currency of any kind. This is a preemptive response to the thought that local or regional bargaining units (i.e. currencies, bartering units, etc) are an effective alternative to global commerce via national and international currencies - in my humble and possibly worthless opinion, they are not.