TVHE has a couple of worries about peak oil. First, oil prices will go up and this could have negative economic consequences. Second, it's a non-renewable resource so we're eating up a capital stock.
It's hard for me to see severe consequences from peak oil.
Hotelling's work on pricing of non-renewable resources remains as salient now as when he wrote it almost 80 years ago. If he's right, we ought just to expect oil prices to rise approximately in line with interest rates, with adjustment upwards if demand is rising faster than that and downwards if technology makes extraction more efficient.
The best case I can think of for breaking Hotelling is that property rights over many oilfields are insecure, or that the ruling juntas in the mid-east have shorter time horizons dictated by keeping political power in the medium term, leading to inefficiently-fast extraction. The best counterargument I can think of is that OPEC seems to work to restrain production, keeping supply now lower than it would otherwise be, and that we're not seeing the big oil companies deciding to just sit on reserves in anticipation of big ramp-ups in prices once the mid-east slows down. If some folks with current rights over oilfields have insecure tenure leading to high discount rates, this leads to locational distortion of production rather than to intertemporal distortion unless those kinds of fields wind up being the whole of the market. And best I can tell, oilfields in the US and Canada are still pumping: if folks expected a big drop in Saudi production, they'd be holding those fields back in anticipation of big price increases to come.
So we shouldn't see sharp spikes upwards as supply dwindles; rather, our best expectation ought to be a steady rise in price. And those kinds of things don't cause big problems.