No Solar Still?

As I see it, there are two major problems with your suggestion of a solar still.

1. It needs a sheet of plastic or some such to work,

2. Because what you collect is condensed water, it doesn't contain minerals and other trace elements your body needs. When drunk in large quantities, it can even drain your body of vital elements. It should be a last resort to survive only, not a got-to method for a default water supply.

What I find more baffling: he neither tried to protect the trickle of water down "his" rock from the sun to minimize evaporation, nor did he attempt to find out where it comes from, i.e., the source of the trickle. If it is wet soil, he could shovel a trench and let the water collect in the bottom, then make a filter of one of his plastic bottles and different layers of moss and sand to drain it and turn it into fresh, drinkable water. That should give him a steady supply.

Also, where do the goats go to drink? And the island's foliage is so thick, it is bound to have an accessible ground water level somewhere, I should think.

Well he did wash up on the island naked, lacking the plastic needed to make a solar still. Also the amount from just 1 still is negligible, realistically you'd want multiple stills.