You need to remove the salt, there's plenty of ways of doing this without re-engineering the human race. However if you want to, I'm sure you can re-apply these to a biological system.
Check out Hypernatremia for all the symptoms that need to be overcome if excessive salt gets into the system. My thinking is filtering before it hits the rest of the system as it makes it much easier than dealing with all the other systems.
Also, even with the only water being the sea doesn't stop you getting fresh water from the air
You can also use the sun to desalinate water and there is good old fashioned hydrolysis if you still have power.