If you read the list many aren't that big of problems to work around, and some are actually benefits that would simply require a modicum of care and forethought such as
these;
Salts freezing. The fluoride salt mixtures have high melting points, depending on the mixture it ranges from 300 to over 600 degrees Celsius. The salts, especially those with beryllium fluoride, are very viscous close to their freezing point. This requires careful design and freeze protection in the containment and heat exchangers. Freezing must be prevented in normal operation, during transients, and during extended station blackouts. The primary loop salt contains the decay heat generating fission products, so these help to keep the salt hot and liquid. For the MSBR, ORNL planned on keeping the entire reactor room (the hot cell) at high temperature, like an oven. This avoided the need for individual electric heater lines on all piping and provided more even heating of the primary loop components.[16](p311). One "liquid oven" concept developed for molten salt cooled, solid fueled reactors, employs a separate buffer salt pool where the entire primary loop is suspended in.[75] Because of the high heat capacity and considerable density of the buffer salt, the buffer salt not only prevents fuel salt freezing, but also participates in the passive decay heat cooling system, provides radiation shielding, and reduces deadweight stresses on primary loop components. This design could also be adopted for LFTRs.
(This allows one of the most promising mechanisms for potential designs, the freeze plug. You have a drain pipe cooled by a blower fan that seals the drain during normal operation, in the event of a power failure the plug would melt and the salt solution would drain into a pan for safe storage. When the reactor is brought online all you need to do is heat the pan and pump the salt solution back into the reactor.)
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Proliferation of Neptunium-237. In designs utilizing a fluorinator, Np-237 comes out with uranium as gaseous hexafluoride and can be easily separated using solid fluoride pellet absorption beds. Theoretically, it should be possible to use Np-237 as fission bomb material. No one has ever successfully produced a bomb with this material, but it should be theoretically possible to use it, because of its considerable fast fission cross section and low critical mass.[85] When the Np-237 is kept in the reactor, it will transmute to Pu-238, an extremely high value fuel for space radioisotope thermal generators.[86] A single gram is worth thousands of dollars. Pu-238 is itself an excellent proliferation deterrent, as explained earlier. Because of this, the Np-237 will likely be sent back to the reactor to be transmuted to Pu-238, which also is a highly sought-after fuel for use in radioisotope thermoelectric generators to power deep-space probes. In addition, it is possible to use vacuum distillation instead of fluorination, which does not separate neptunium at all. It should be noted, that all reactors, not just thorium reactors, produce considerable amounts of neptunium, which is always present in high (mono)isotopic quality, and it is just as easily extracted chemically.[85] This is therefore not a distinguishing issue for LFTRs in particular. In fact, americium could also be theoretically used for nuclear weapons,[85] and LFTRs do not produce meaningful quantities of americium, indeed they are one of the few reactor types that can burn existing stockpiles of americium and neptunium with high efficiency.[46]
(This ties in with the different fuel cycle economic concerns, pu-238 is a valuable and marketable material.)
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Waste management. There is also a need to manage the waste, which is still very radioactive, even though it is hazardous for a shorter period. Because some fission products, in their fluoride form, are highly water soluble, fluorides are a less suited long term storage form. For example, cesium fluoride has a very high solubility in water. For long term storage, conversion to an insoluble form such as a glass, could be desirable.
(Compared to waste management for our current reactors this would be a welcome change, current waste could even be transmuted to safer forms using these types of reactors.)
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The solubility for plutonium is limited. The fluorides of plutonium, americium, and curium, occur as trifluorides, which means they have three fluorine atoms attached (PuF3, AmF3, CmF3). Such trifluorides have a limited solubility in the FLiBe carrier salt. This makes startup on these transuranic wastes more difficult especially for a compact design that uses a smaller primary salt inventory. This solubility can be increased by operating with less or no beryllium fluoride (which has no solubility for trifluorides) or by operating at a higher temperature (as with most other liquids, the solubility goes up with temperature). A thermal spectrum, lower power density core does not have issues with plutonium solubility.
(the fact that you would be easily able to bring marketable materials out of solubility by regulating temperature is actually a good thing.)