According to Oliver Tickell, not much:

Numerous advantages for thorium as a nuclear fuel and for the LFTR design over conventional solid fuel reactors have been claimed. In this section we consider each of these claims in turn.
3.1 Abundance of thorium relative to uranium
Claim: Thorium is several times more abundant in the Earth’s crust than uranium.
Response: Thorium (232Th) is indeed more abundant than uranium, by a factor of three to four. But whereas 0.7% of uranium occurs as fissile 235U, none of the thorium is fissile. The world already possesses an estimated 1.2 million tonnes of depleted uranium (mainly 238U), like thorium a fertile but non-fissile material. So the greater abundance of thorium than uranium confers no advantage, other than a very marginal advantage in energy security to those countries in which it is abundant.
3.2 Relative utility of thorium and uranium as fuel
Claim: 100% of the thorium is usable as fuel, in contrast to the low (~0.7%) proportion of fissile 235U in natural uranium.
Response: Thorium must be subjected to neutron irradiation to be transformed into a fissile material suitable for nuclear fuel (uranium, 233U). The same applies to the 238U that makes up depleted uranium, which as already observed, is plentiful. In theory, 100% of either metal could be bred into nuclear fuel. However, uranium has a strong head start, as 0.7% of it is fissile (235U) in its naturally-occurring form.
3.3 Nuclear weapons proliferation
Claim: thorium reactors do not produce plutonium, and so create little or no proliferation hazard.
Response: thorium reactors do not produce plutonium. But an LFTR could (by including 238U in the fuel) be adapted to produce plutonium of a high purity well above normal weapons-grade, presenting a major proliferation hazard. Beyond that, the main proliferation hazards arise from:
the need for fissile material (plutonium or uranium) to initiate the thorium fuel cycle, which could be diverted, and
the production of fissile uranium 233U.Claim: the fissile uranium (233U) produced by thorium reactors is not “weaponisable” owing to the presence of highly radiotoxic 232U as a contaminant. Response: 233U was successfully used in a 1955 bomb test in the Nevada Desert under the USA’s Operation Teapot and so is clearly weaponisable notwithstanding

any 232U present. Moreover, the continuous pyro-processing / electro-refining technologies intrinsic to MSRs / LFTRs could generate streams of 233U very low in 232U at a purity well above weapons grade as currently defined.
3.4 Safety
Claim: LFTRs are intrinsically safe, because the reactor operates at low pressure and is and incapable of melting down.
Response: the design of molten salt reactors does indeed mitigate against reactor meltdown and explosion. However, in an LFTR the main danger has been shifted from the reactor to the on-sitecontinuous fuel reprocessing operation – a high temperature process involving highly hazardous, explosive and intensely radioactive materials. A further serious hazard lies in the potential failure of the materials used for reactor and fuel containment in a highly corrosive chemical environment, under intense neutron and other radiation.
3.5 State of technology
Claim: the technology is already proven.
Response: important elements of the LFTR technology were proven during the 1970s Molten SaltBreeder Reactor (MSBR) at Oak Ridge National Laboratory. However, this was a small research reactor rated at just 7MW and there are huge technical and engineering challenges in scaling up this experimental design to make a ‘production’ reactor. Specific challenges include:
developing materials that can both resist corrosion by liquid fluoride salts including diverse fission products, and withstand decades of intense neutron radiation;
scaling up fuel reprocessing techniques to deal safely and reliably with large volumes of highly radioactive material at very high temperature;
keeping radioactive releases from the reprocessing operation to an acceptably low level;
achieving a full understanding of the thorium fuel cycle.
3.6 Nuclear waste
Claim: LFTRs produce far less nuclear waste than conventional solid fuel reactors.
Response: LFTRs are theoretically capable of a high fuel burn-up rate, but while this may indeed reduce the volume of waste, the waste is more radioactive due to the higher volume of radioactive fission products. The continuous fuel reprocessing that is characteristic of LFTRs will also produce hazardous chemical and radioactive waste streams, and releases to the environment will be unavoidable.
Claim: Liquid fluoride thorium reactors generate no high-level waste material.
Response: This claim, although made in the report from the House of Lords, has no basis in fact. High-level waste is an unavoidable product of nuclear fission. Spent fuel from any LFTR will be intensely radioactive and constitute high level waste. The reactor itself, at the end of its lifetime, will constitute high level waste.

Claim: the waste from LFTRs contains very few long-lived isotopes, in particular transuranic actinides such as plutonium. 

Response: the thorium fuel cycle does indeed produce very low volumes of plutonium and other long-lived actinides so long as only thorium and 233U are used as fuel. However, the waste contains many radioactive fission products and will remain dangerous for many hundreds of years. A particular hazard is the production of 232U, with its highly radio-toxic decay chain.

Claim: LFTRs can ‘burn up’ high level waste from conventional nuclear reactors, and stockpiles of plutonium.
Response: if LFTRs are used to ‘burn up’ waste from conventional reactors, their fuel now comprises 238U, 235U, 239Pu, 240Pu and other actinides. Operated in this way, what is now a mixed-fuel molten salt reactor will breed plutonium (from 238U) and other long lived actinides, perpetuating the plutonium cycle.
3.7 Cost of electricity
Claim: the design of LFTRs tends towards low construction cost and very cheap electricity.
Response: while some elements of LFTR design may cut costs compared to conventional reactors, other elements will add cost, notably the continuous fuel reprocessing using high-temperature ‘pyro-processing’ technologies. Moreover, a costly experimental phase of ~20-40 years duration will be required before any ‘production’ LFTR reactors can be built.
It is very hard to predict the cost of the technology that finally emerges, but the economics of nuclear fuel reprocessing to date suggests that the nuclear fuel produced from breeder reactors is about 50 times more expensive than ‘virgin’ fuel. It therefore appears probable that any electricity produced from LFTRs will be expensive.
We must also consider the prospect that relatively novel or immature energy sources, such as photovoltaic electricity and photo-evolved hydrogen, will have become well established as low-cost technologies long before LFTRs are in the market.
3.8 Timescale
Claim: Thorium and the LFTR offer a solution to current and medium-term energy supply deficits.
Response: The thorium fuel cycle is immature. Estimates from the UK’s National Nuclear Laboratory and the Chinese Academy of Sciences (see 4.2 below) suggest that 10-15 years of research will be needed before thorium fuels are ready to be deployed in existing reactor designs. Production LFTRs will not be deployable on any significant scale for 40-70 years.