I didn't want my first post to be argumentative but I might have known it would be. Oh well.
I'm not entirely comfortable with Arjen's summary. I don't want to nitpick so will just mention a couple of things. The example of a dialetheia is misleading because it does not describe a true contradiction. A true contradition would be Heraclitus's 'We are and are not.' This seems to me one of the most radical and important statements in philosophy. Perhaps it is a stronger statement of his seemingly paradoxical philosophical position than the one you mention, as it is not clear that the seawater example is a paradox in a philosophical sense.
Sorry to start by not agreeing. What I would agree with is the importance of the topic.
Could we define a true paradox as an intellectual dilemma, or is that a tautology?