Does the salt in the ocean act as a binding agent on sand?
Good observations!

Seawater contains salts in small amounts such as such as $\ce{LiCl}$ and $\ce{MgCl2}$ that are quite hygroscopic, which could keep the sand wet longer.

There is also dissolved organic matter (http://www.eoearth.org/view/article/154471/) in seawater that might act as a hydrating agent or as a wetting agent, helping to hold onto the water and to bond it to the sand.

You might try an experiment comparing the appearance of (washed) sand after being wet with plain water, with $\ce{NaCl}$ salt water of the same concentration as seawater, and with seawater itself to see if there is a difference. Though this seems like a casual test, this could be of significance in cases where it's necessary to drive on a sandy shore.