The main concern are arsenic and mercury which accumulate in bottom feeding sea critters some of which we eat (mainly shellfish and shrimp). The uptake of uranium are thorium in marine species is rather low, but yes, burning coal also spreads radiation. Some of the byproducts of nuclear fission (I131, Sr90) are more dangerous because they tend to stick around in our bodies. Uranium and thorium get excreted but the first one is also toxic.

Of the two Radon isotopes, one has a half life of 55 seconds, the other 2.5 days. The main problem are its decay products: Pb210, Bi210 and Po210. It's better to vent it off into the atmosphere than to let it accumulate in mines and basements.