mdsolar's point isn't that we should build no new nuclear, at least not in this thread. His point is that nuclear can't, in and of itself, decarbonize the electric sector. We simply don't have the capacity to build that many nuclear power plants simultaneously, nor do we have the fuel, nor do we have the money.
The first one might be overcome. After all, if world leaders were able to simultaneously lay out this plan and get political support for it, part of the plan would include training more engineers, trades, and other jobs necessary. We might not be able to build 100 per year in 2016 (or even 2020), but we could ramp up.
The world went from building roughly zero a year in 1960 to building 26 a year by 1967, and even then was not an all-out worldwide construction effort. Ramping up large scale construction over a 35 year period should be no real trick, if the funds and will are available.
The second one might be overcome. After all, with pressure for more fuel, we might go out and find more fuel, develop new techniques to find, recover, and process more fuel, etc. I doubt we could overcome it, but generally speaking if we went "long" on nuclear, at least some more fuel would turn up.
Lots of fuel has already turned up. Enough for 5,000 years of once-through burning, no breeding or reprocessing. It is in the sea. Technologies have been demonstrated that can extract uranium at about the same price point as uranium spot prices that have already been encountered. The cost of uranium fuel is a very small part of the cost of nuclear electricity, and even if the uranium-from-seawater costs never come down (though surely they will), it does not have an important impact on the cost of nuclear electricity.
The third one is the toughest. Nuclear power, today, is more expensive than wind and in some places, more expensive than solar. Given that wind and solar don't have the political opposition, don't have 10-15 year lags from "let's build it" to "let's turn it on", and can be built in more places at far smaller increments, it's really tough to argue that we should spend the money on nuclear when there are cheaper options.
Right, this is the true Achilles heel of nuclear power. The high capital costs, and the long pay-back time. Only intervention by national governments can get large scale power plant construction to happen. The market will never do it. It is important to focus on the true fundamental issue if nuclear power is going to contribute more to zero carbon electricity.