What practical issues remain for the adoption of Thorium reactors?

I was going to comment on other people's answers, but this was going to become too long.

Almost everyone fails to separate Thorium (which is a fuel type) and reactor type. Safety is a function of the reactor type, and molten salt in particular for this question. Does the fuel choice impact ultimate reactor safety? Yes, but to a limited extent. So how does the use of Thorium as a fuel impact the ultimate reactor safety? Here:

1. Thorium basically only has one natural isotope. This reduces the number of heavy element chemical species that must be dealt with in a chemistry system. This makes it more suitable for a molten salt reactor than most fuel cycles, which most people believe is a very safe design.
2. Thorium produces very few neutrons per fission. In fact, it's only like 2.3 when others are closer to 3.0 (but not quite there). Does that impact safety? Maybe. Since there are so few neutrons, any critical configuration has less physical capability to go dangerously supercritical, but I wouldn't emphasize that point too much. The more important factor here is that the scarcity of neutrons makes it hard to make weapons. You need 1 to breed so you're left with 2.3-1 = 1.3 and you only have 0.3 neutrons per fission lose to the environment (or breed extra) and this is difficult to manage. Also, anything that is more neutron-efficient has fewer activation products so is a less radioactive plant. Generally, without extra neutrons those extra neutrons aren't causing trouble.
3. Thorium produces somewhat less dangerous fission products. No matter what nuclear fuel cycle you use you still have to deal with the fission products because they are the direct result of the fission reaction just like CO2 is a direct product of combustion reactions. Thorium is said to have FPs that are a little easier to deal with over long term, but I think the difference is very very marginal. This can improve the safety of the waste.
4. Thorium can be breed at thermal energies. This is such a major point that it is an oversight to not mention. Thorium is unique among the potential fuels in that a thermal reactor can breed new (fissile) fuel in perpetuity. Thermal reactors are smaller, cheaper, easier to deal with, and probably safer. We currently use thermal Uranium-Plutonium reactors that breed at less than breakeven. A Thorium-Uranium reactor can breed at thermal energies at higher than breakeven.

Now, Thorium is vastly more sustainable than natural Uranium, we all agree on that. But the problem with nuclear power today is not sustainability of the fuel supply. Your question is why we haven't adopted it as a power source. To start with, we have no economic reason to adopt it. You could ask why we have not adopted the molten salt reactor, for which the answer is a matter of technology evolution. Also, we don't have many breeding reactors in general which is tied to larger issues like reprocessing. Thorium fuel cycles offer their own unique approach to a breeding fuel cycle. But to use Thorium is to use breeding, and we don't do (deliberate) breeding.

At the same time that Thorium has advantages, it has disadvantages. The small number of neutrons per fission is a drawback for the design of the reactor. The company Terrapower proposes to make a candle-type reactor with U-238. You could not do this with Thorium because it doesn't have enough neutrons. The design isn't neutron-efficient enough. A molten salt rector (MSR), on the other hand, is one of the most neutron-efficient designs we've ever contemplated. Obviously it matches well with Thorium. U-238 could be used in a MSR as well, but Thorium could not be used in a Terrapower design.

To summarize my opinion, there is a strong argument for Thorium based on sustainability, there is a weak argument for Thorium based on the waste, and there is really no argument for Thorium based on economics. Current designs are based on economics. QED.

I'm not sure what all you've read on them, but I'll try to clarify at least a few things. I would certainly disagree with several of your assertions.

For starters, you say "...they don't produce anything you could feasibly use as a source of material for nuclear weapons." Thorium reactors use Thorium as a fertile fuel that transmutes into fissile U233. While the spent fuel does not contain the same ratios of elements as a uranium fuel cycle, it does indeed contain bomb worthy isotopes as well as some longer lived fission and daughter products. In fact, the thorium cycle was used to produce some of the fuel for Operation Teapot in 1955.

You say "...they're far less prone to catastrophic failure..." While it may be the case that thorium reactors have traditionally had fewer catastrophic failures than uranium reactors, it is also true that the statistics are too small to make reasonable conclusions as to the reliability of such systems. To my knowledge, no commercial reactors use a thorium fuel cycle. In other words, all of the thorium reactors are one-off, uniquely designed pieces of equipment with well trained and knowledgable working staff.

There are roughtly 435 commercial nuclear plants in operation with another 63 under construction. There have been on the order of 20 major nuclear accidents over the years. There are only 15 thorium reactors. Statisitcally, thorium reactors might have a worse accident rate.

There is certainly ongoing research into commercial applications of a thorium fuel cycle. Interestingly, as that article suggests, a thorium cycle requires another isotope to get the reaction going so there will always be a need for some uranium cycle reactors. Like P3trus said, even outside of India (where the thorium reserves provide good economic incentive) there are people considering thorium.

Ultimately, the preference for a uranium fuel cycle is a pragmatic one. The nuclear industry has a great deal of experience with uranium. It's true that there is more thorium than uranium, but uranium is hardly rare. It is sufficiently common, in fact, that there aren't even very many estimates of the size of the reserves.

With respect to public opinion, thorium does not offer a tangible difference to uranium other than a change of name. As long as public opinion is against nuclear, that will include thorium. If they turn to support nuclear, the economics still point to uranium.

The German THTR-300 Thorium High-Temperature Reactor operated for about 16,000 hours and the IAEA produced a report on its shutdown.

So there are no physics barriers to thorium reactors: there is an existence proof for thorium reactors.

That ends the relevant answer for this site.

There are economic, engineering, social, political, technical, and institutional barriers; and large quantities of hype and incorrent information on the subject; but none of those are relevant to this site.