What do the descriptions in verse 13 refer to in Paul's defense?
The descriptions refer to false teachers and their empty, corrupting message—clouds without water, withered fruit, raging waves, and wandering stars. Paul uses them as a contrast in his defense, insisting he did not come corrupting God's Word, with half-truths, or as one foaming out shame.
Les explains that these are all descriptions of what Paul says he was not. In II Corinthians, verse 17, Paul again defends his apostleship by saying he did not come corrupting the Word of God and did not come with half truth. Les illustrates false teaching like a little puff of cloud during drought that brings hope but disappears, like clouds without water carried about with wind, trees whose fruit withereth, a raging wave of the sea foaming out its own shame, and wandering stars reserved for blackness of darkness forever. The world is falling for that adulterated line of false teaching, but Paul contrasts his ministry with it.
These are spots in your feasts of charity, when they feast with you, feeding themselves without fear: clouds they are without water, carried about of winds; trees whose fruit withereth, without fruit, twice dead, plucked up by the roots;
Raging waves of the sea, foaming out their own shame; wandering stars, to whom is reserved the blackness of darkness for ever.