You make a lot of really good points about the situation in the Middle East and Iran. I mostly agree, but I have to dissent on some issues, not all, and I will expand on some on your points.
First, the Iran's case, as I wrote few days ago, I really doubt that the Iranian government will fall any time soon, for one simple reason: the political elites (Ahmadinejad, in particular) still have very strong support from the military, notably the Republican Guard, and a bunch of Mullahs. Yes, there are splits in the religious leadership, as the crackdowns that Ahmadinejad authorized was not totally supported, and his hounding of two major religious figures, regardless whether they are in opposition or not, are very disturbing to the rest of mullahs. Like it or not, these two used to be Khomeini's comrades, and thus they had some sort of prestige.
On the other hand, with the military remains firmly behind Ahmadinejad, ready to crack down the protesters, I doubt that there will be a "Jasmine Revolution." It happened in Tunisia, Egypt, and Libya because the governments are completely divided, or in Libya's case, there's no effective functioning government at all. Iran will be a different story.
While you are right about the Sunni-Shia thing, one aspect of Mueller's argument that you neglect to mention is how a small dedicated well-armed gangsters can terrorize and control the population. (I am not going to delve into his Yugoslavian case study, lest it distract us from this conversation.) The Iranian government can pick and fund one small and yet dedicated group to annoy and instigate trouble in other countries. It has done that in Iraq (al-Sadr), Lebanon (Hizbollah) and Palestine (Hamas). In Hamas case, it shows that such influence can transcend religious divide. Also keep in mind that Iraq under Saddam Hussein was a Sunni minority government controlling a Shia majority country, and not to mention the political and military elites of Bahrain are all Sunni minorities.
It is true that having overthrown one dictatorship, the Egyptians and Tunisians won't be that stupid to jump into a Mullah's hand, let alone a discredited bunch such as the Iranian Theocracy. On the other hand, with enough funding from and business ties to Iran could over the long run, countries in the region could be eventually controlled and dominated by Iranian interests.
What really worries me at this point is whether the United States will be able to maintain its influence in the region. I think it is true that a huge majority of the protesters are mostly concerned about economic needs and fed up with the sluggish and rotten ancien regime that currently presides over them. Still, it does not stop some exasperated autocrats (e.g. in Yemen) to claim that the United States and the Jewish conspiracy is to blame for their woes. Also disturbingly, there are rumors circulating that Qaddafi's mercenaries are mostly Israelis or at least trained by the Israelis, showing that old habits of creating a bogeyman, regardless of the circumstances, die pretty hard. Of course, the seemingly incoherent US responses to the crisis do not help.
When the dust settles, I don't doubt that there some rabble-rousers will try to attack the new governments by linking them to the American interests, like what we have seen in Pakistan. If you don't think that this is important or could not happen, then you should read Jack Snyder's From Voting to Violence. It is a good book, though not without flaws, but it has good insights. Stephen Walt's Revolution and War also highlights a plausible worst-case scenario, in which revolutionary Egypt may decide to wage external wars to unite the country.
So whether Iran will end up as big winner, I'd say it depends in the next a few months, when these countries recovering from upheaval start building their governments. Of course, the best case scenario is that most militants or radical groups understand what people really want is freedom, economic growth, and good governance. It seems that Ikhwanul Moslem (or the Moslem Brotherhood) in Egypt has been taking this lesson to heart. On the other hand, if the transitional governments make massive mistakes, things may blow up and you can get various worst case scenarios, from civil war to a really weak government (like Pakistan).