What practical issues remain for the adoption of Thorium reactors? From what I've read on thorium reactors, there's enormous benefit to them.  Their fuel is abundant enough to power human civilization for centuries, their fission products are relatively short-lived, they're far less prone to catastrophic failure, and they don't produce anything you could feasibly use as a source of material for nuclear weapons.  
So what technical issues need to be resolved so that Thorium reactors become practical and put into wide use?  Is it purely engineering issues that need to be overcome?  Or are there problems of physics as well?  If so, what are the technical problems and what research is occurring to overcome them?  
If none of the problems that face thorium reactors are insurmountable, then why aren't they the focus of research and development that nuclear fusion is?  Are there real environmental issues? (If so what are they?)  
 A: The short answer is no. There are some advanced materials and engineering to apply, but I have yet to find any scientific road blocks.
The long answer involves cold-war history, bureaucratic inertia and other off-topic factors, so I will skip ahead to explain why thorium's benefits include the molten-salt design:
The chemistry of thorium differs from the chemistry of uranium. Thorium can only be oxidized to +4, and ThF4 remains a liquid in the LFTR a breeding reservoir. Protactinium and uranium oxidize higher, and their higher fluorides turn to gas at LFTR operating temperature.
This difference gives reactor designers the opportunity to transmute fertile thorium and then separate the products (and by-products) from the breeding stock (rather than removing the breeding stock from the products). We can't do that with uranium bred up to plutonium; they both form gaseous hexafluorides. For that reason, molten-salt reactor designs are ideal for thorium but impractical for uranium.
Once we see that practical molten-salt designs are exclusive to thorium, then we understand why all of that design's advantages attach to the fuel choice. Advantages include:


*

*A fluid core can have neutron poisons removed so that higher burn rates can be achieved. Solid-fuel reactors typically burn only about 1% of their fuel. Molten-salt designs may well burn 99%.

*Breeding thorium and then burning nearly all of the fissile fuel leaves virtually zero higher actinides (i.e. long-lived plutonium waste) in the eventual slag. In fact, much existing plutonium waste could be destroyed in a plutonium-core + thorium-jacket design that a government might employ to prime the pump of an incipient LFTR industry.

*In a LFTR, a meltdown is a walk-away auto-shutdown mechanism, not a disaster.

*LFTR is a low-pressure design (no super-heated water looking to expand a thousand times). That means smaller, easier, far less costly containment than with BWR designs.

*A liquid core enables easier by-product extraction, before useful isotopes decay away. 
A: 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.
A: I'll presume your question is more specifically why aren't we building molten salt thorium reactors (aka LFTRs).  First to correct a few statements.


*

*"their fission products are relatively short lived."  The fission products from any nuclear reactor are pretty much the same.  BUT a key difference from light water reactors (LWRs) is that a LFTR fed with thorium will produce significantly less (about 20x less) plutonium than an LWR.  Further, it is more feasible to recycle the plutonium back into the reactor and burn it up.  It is the plutonium and other transuranics (TRUs) like Americium and Curium that are the serious problem in nuclear waste disposal.  So while the fission product wastes are the same, the problematic TRU waste problem is significantly improved with LFTRs.

*weapons use - depends very much on the specifics of the design - some versions of LFTRs are the most proliferation resistant of any nuclear power plant - and I could imagine others that would be ideal for producing weapons grade fuel.
Depending on the design there are some challenging questions - making the first reactor wall stand up to the neutron bombardment, making a fluorinator vessel that withstands the fluorine gas for separating uranium while being hot enough to keep the salt molten, being sure the tritium doesn't leak out, separating the plutonium from fission products (at a secure facility) are a few that come to mind.  I don't think any of these require breakthrough science but are more along the lines of R&D engineering.
None of these reasons are sufficient to prevent development of the reactor though.  The reactor development will require some substantial money (\$1B to a large scale prototype and \$5-10B to get the first of a kind commercial reactor).  The reactor is different than LWRs and will require different regulations.  Any investment has a significant risk that the regulations won't be reasonable or even developed.  The investment also will take a long time to payout - likely more than 10 years even with an aggressive plan.  So it is a very difficult sell to private investors (though not impossible as there are a few small scale private efforts ongoing today).
Practically, the question is what prevents the government from making any serious investment in next generation reactors and why is it so very conservative?  These aren't physics questions.
The blunt answer to your question is that physics is not what holds up LFTR.
A: 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:


*

*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.

*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.

*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.

*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.
A: I am just augmenting the answer of AlanSE by one point - 
One huge disadvantage of thorium is that Thorium has Thallium 208 as one of the daughter product, this is a high gamma emitter.
$$Th_{232}^{91} + n_1^0 = U_{233}^{92}$$
but sometimes one can also expect $U_{232}^{92}$, which has a falf life of 62 years and has $Tl_{208}$ and $Tl_{228}$ in daughter products list. The former a hard gamma emitter and latter an alpha emitter.
This feature on one side is an advantage because then it would be impossible for smugglers to smuggle out fuel rods through radiation monitors and non-proliferation can be better achieved.
But on the other hand, it causes serious concerns with the fuel fabrication cost, both in terms of the man-rem and technological cost.
A: 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.
A: They are considered in new reactor types. E.g. the generation 4 molten salt reactor is particularly suitable for the thorium fuel cycle.
A: Building a nuclear reactor is very large-scale investment, and as thorium reactors are unproven, and there is already a large infrastructure in place for the uranium fuel cycle (mining, purification, enrichment, rod fabrication, etc...) a uranium reactor is considered a safer investment.
A: The ideal approach to take with thorium breeder reactors, which can also enable these reactors to use U-238 as breeder fuel, too, is to design these commercial breeder reactors to use continuous thermonuclear triggers as a primary source of neutrons. Hybrid nuclear/thermonuclear breeder reactors which use continuous thermonuclear triggers will also be able to burn most (approx. 80%) of their nuclear waste as fuel, too. This means that we will be able to use 100% of Uranium and 100% of Thorium as breeder fuels, combined with approx. 80% of nuclear waste as nuclear fuel, too, which in turn will provide many thousands of years of energy for our planet in the future, while also solving global warming at the same time.
A: The opposition to recycling spent nuclear fuel- for either plutonium from irradiating 238 U or 233U from irradiating Th- is a major impediment.  There is much more experience in reprocessing for Pu than for Th - due to the weapons programs- so if reprocessing ever gains wide acceptance it will probably be for Pu.
