My finished chocolate has tiny white spots. What could cause this?

That’s what we call bloom - if it is crispy to touch it’s sugar bloom, if oily it’s fat bloom.

Sugar bloom is usually the result of leaving chocolate in the refrigerator then when you take it out condensation forms on the surface.  The sugar in the chocolate dissolves in the condensed water and as the water evaporates, the sugar comes out of solution, resulting in crystals on the surface of the chocolate.

Fat bloom can result from poor temper or a fatty center that is leaking oil through the shell.