There are some major changes that Paul could make unilaterally. He really could recall U.S. troops from not only Iraq and Afghanistan, but all over the world. I believe he would really do so, and despite the radicalism of this change, I'm confident that these orders, however unpopular, would be obeyed. Perhaps there would be a 2% chance of a coup if he made the changes overnight, but that's about it.
Furthermore, there are a number of "executive order" policies that he could change with the stroke of a pen. If I understand the law correctly, the president could unilaterally end affirmative action in federal hiring (and the hiring of federal contractors). And he could probably stop federal prosecutions for the sale of medical marijuana.
So what else could President Paul do on his own? He certainly couldn't abolish the Federal Reserve or return to the gold standard on his own, so whatever you think about that plan, it's not going to happen. In fact, Paul could not abolish any law unless half of both houses of Congress went along with him. And since he is probably the most libertarian politician in either house, almost all of the laws Paul wants to abolish would survive his presidency.
What Paul could do is stop or dilute new laws, including the budget. If you want to abolish old laws, gridlock works against you; but if you want to stop new laws, gridlock works in your favor. No new law could pass unless 2/3 of both houses wanted it. Given Paul's extremism, his opponents would have to heavily moderate any new statist legislation to make it veto-proof. The same goes for the budget: Since Dr. No would probably veto any budget that Congress would pass, fiscal conservatives could and probably would hold out for substantial spending cuts. And this is on top of the massive peace dividend Paul's unilateral foreign policy changes would realize.
Bottom line: Even if, like Megan McArdle, you think that Paul is "utterly insane," anyone with moderate libertarian sympathies (and no desire to crusade against "Islamo-Fascism") would probably be pleased by the policy consequences of Paul's presidency. In fact, it would take a radical like Paul to get moderate libertarian change.
Gee, it's almost as if the Constitution had built-in checks and balances!