We put up some composite trim using an 18 gauge air nailer, however, some of the nails did not go in all the way, mostly due to operator inexperience. What's the best way to cover up/remove the nails that are not countersunk? And after they get countersunk, what's the best thing to fill the holes with? This will be in a wet location.
Countersink with a nailset, struck with a hammer.
Fill with painters caulk.
As for the second question regarding filling the holes after countersinking:
Use DAP Painter's Putty '53' - pull out a portion the size of a large marble, shape it into a sphere or ball, and then use it like an eraser on your countersunk nail holes. If you rub the putty ball back and forth along your trim over the countersunk nail hole, you'll slowly fill the hole with the putty and leave a smooth surface appropriate for painting.