Right now I'm having trouble finding many, other than people who:
1- are terrified of anything 'atomic', and
2- work for competing energy creators
These are listed on Wikipedia (grain of salt - HAR!):
- Little development compared to most Gen IV designs.
- Required onsite chemical plant to manage core mixture and remove fission products.
- Required regulatory changes to deal with radically different design features.
- MSR designs rely on nickel-based alloys to hold the molten salt. Alloys based on nickel and iron are prone to embrittlement under high neutron flux.
- Corrosion risk.
- As a breeder reactor, a modified MSR might be able to produce weapons-grade nuclear material.
- The MSRE and aircraft nuclear reactors used enrichment levels so high that they approach the levels of nuclear weapons. These levels would be illegal in most modern regulatory regimes for power plants. Some modern designs avoid this issue.
- Neutron damage to solid moderator materials can limit the core lifetime of an MSR that makes moderately fast neutrons. For example, the MSRE was designed so that its graphite moderator sticks had very low tolerances, so neutron damage could change their size without damage. "Two fluid" MSR designs are unable to use graphite piping because graphite changes size when it is bombarded with neutrons, and graphite pipes would crack and leak.
It's really an elegant way of generating energy, though there are disadvantages. There's no free lunch, but I believe something like this will be the future of electrical power generation.