Superheated liquid metal is very reactive with water or moisture and creates hydrogen gas.
Which is why they take great care in keeping water from it. Seriously though, there are concerns about water getting to the liquified metal and it could be quite a problem if it got out of hand. I do recall that in an experimental reactor in Japan they had pools of liquid metal that were open to the air without much concern, the metal would form a "crust" that prevented further oxidation. This is much like a tarnish on a solid metal forming. This worked well in that Japanese reactor until a crane fell into one of the liquid metal pools. That was pretty much the end of that reactor.
Liquid salt is corrosive.
Largely a myth. Tests show that use of fairly common alloys will hold up to the salts used in these planned reactors for decades. Of course we won't know for sure if it will hold up for decades until it is actually tested for decades but this is a largely solved problem.
Graphite moderator burns in atmosphere and made Chernobyl accident worse.
Also largely a myth. Graphite is pure carbon, much like coal. Unlike coal the graphite used as a moderator is in a metallic state. As a metal is it highly conductive, making it difficult to get hot enough to ignite. As a metal it's not "rough" like coal and does not give much surface area to oxidize. If hot enough, long enough, with enough air, it will start on fire. However, at that point the reactor will already have been destroyed from whatever made it that hot to begin with. Also, there just isn't a lot of graphite in these reactors. The heat from burning graphite is a rounding error if there is ever a problem of something burning.
No matter what clever materials you use, no fission reactor is inherently safe, unless it is some sort of subcritical reactor, so that you don't act upon it to keep its chain reaction stable, but instead continuously supply energy to it to produce more energy.
When it comes to molten salt reactors a common safety element is the "freeze plug". This is a section of pipe at the bottom of the reactor vessel that is kept cool to plug the pipe. This pipe drains to a tank which is in a shape that prevents fission, removed from the moderator, and kept cool with passive systems. If power is lost the plug thaws, the reactor drains, and fission stops. If the reactor gets too hot the cooling system that freezes the plug is overwhelmed, the plug thaws, the reactor drains, and fission stops.
Some designs go an extra mile and allow for the unlikely event the freeze plug fails. This is done by having the moderator rods getting inserted from the bottom of the reactor and held up by electric motors. If power is lost then gravity lowers the moderator from the reactor and fission stops. Another fail safe which is rarely mentioned is that the alloy that the reactor vessel is made of has a melting point lower than the boiling point of the salt it holds. If for some reason the reactor got really hot the vessel would melt away and release the salt into the drain pan below it, which drains to the same drain tank that the freeze plug would open into.
I've seen a few sub-critical reactor designs and a common feature on them are scram rods. Why would a sub-critical reactor need to have scram rods? At least I asked myself this question. The reason is that these reactors are held so close to critical that it is possible for it to go super-critical in a split second. If this is not accounted for with a means to scram beyond just shutting down the accelerator then it would never get licensed. If built so that it was further from critical mass so scram rods are not needed then the accelerators need to be so large as to become impractical. Which means, in short, sub-critical reactors are impractical.
Molten salt reactors are much like accelerator driven reactors in that if power is lost the reaction stops. The difference is in the power required to keep the reactor going. In an accelerator driven system it takes a large fraction of the power produced, in a molten salt reactor the power required is in the noise.