The main concern when defrosting frozen fish is food safety. By that we mean minimizing the growth of bacteria that can cause food poisoning. And it turns out that the most efficient ways to defrost fish also happen to be the safest.
Both the refrigerator method and the cold water method are designed to keep fish out of the food safety danger zone of 40 F to 140 F—it’s at these temperatures that bacteria grows the fastest. As with all perishable foods, never leave raw or cooked fish at room temperature for more than 2 hours, or more than 1 hour if the temperature is above 90 F.4
Also be sure to wash your hands before and after handling the fish, to thoroughly clean any tools or surfaces that touched the fish, and to discard the packaging the fish came in or that you transferred it to.
Once thawed, fish can sometimes have a mushy texture. This can happen if you submerge the fish directly in water without tightly sealing it in plastic
Fish, like all living things, is made up of millions of cells, and these cells contain liquid. When fish is frozen, that liquid also freezes. If the freezing process happens too slowly—i.e. if the fish wasn’t flash-frozen properly—that liquid can form ice crystals that will rupture the cells of the fish. When that fish is later thawed and cooked, this liquid will leak out, producing a mushy texture.
Thicker steaks and fillets, because they take marginally longer to freeze, are more likely to have this issue, although if it’s been frozen properly, it shouldn’t be a problem. But assuming you defrosted it properly, if this does happen, it was most likely caused by something that occurred before you bought the fish, not by the way you thawed it