The starch in potatoes is stored in starch granules. When you cook potatoes the starch granules will be destroyed, the starch is liberated and becomes soft. A potato is well cooked when all starch granules are destroyed.

The starch in the granules is surrounded by a layer of polysaccharides, called hemicelluloses. The main hemicellulose substance is pectin. For a potato to be cooked properly these hemicelluloses have to be destroyed. Normal salt (sodium chloride) has no effect on the hemicelluloses. Potatoes cooked in water with a lot of salt will cook normally. Calcium salts on the other hand strengthen the pectin structure. Therefore, calcium is added to many canned vegetables to prevent softening of the products. Seawater only contains traces of calcium, but a rather high concentration of magnesium. Magnesium also can strengthen the pectin structure but not as strongly as calcium.

Thus when you cook potatoes (or vegetables) in seawater the magnesium will strengthen the pectin structure, which makes cooking and softening of the product much more slowly or even impossible.

In different parts of Europe traditionally potatoes are cooked in seawater, but in most cases the seawater is first diluted with fresh water. This reduces the magnesium content and the potatoes will cook properly. Similarly, there are considerable differences between the different varieties of potatoes, which also influence the effectiveness of the magnesium.