I think it has to do with calculation of reflections and transparency when 'faces' are very near to eachother. You also get black edge lines when making very shallow water e.g. (talking centimeters/millimeters), and higher subdivision settings (up to 1) and higher detail settings do help to get them out.
For water that doesn't really need transparency, you could also try a reflective shader replacing the reflections of the water shader (and transparency to zero), and use smooth (0.004) reflections.