Smooth, is probably the first thing I look for. I can tell by the way they drive up and jockey into position. To get your neck snapped back when leaving the ground, and then left swinging back and forth 15 to 20 feet while slowly spinning in a circle trying to give hand signals is not my idea of a smooth entry into the tree.
Quiet confidence is nice to see. The new guy trying to impress is worse than the done it all know it all; neither is a team player. I like to take a minute or two, question pick weights at different distances, and agree on a basic plan to take this tree apart in 3 or 5 or 9 picks. Then we start working together.
Having "The touch" is really nice when pre-tensioning a pick, or gently lifting a trunk section so you never have to hear the sound of cable slapping boom. Pieces rigged right seem to just float away. Some new guys have it, some vets never will.
Nice to hear a "thank you" for helping get set up, dunnage, rigger pads, freeing dead section etc. BUT the crane op that says quietly "thanks for makin me look good", well, I can't wait to work with him again... ; ^ )
By the way, thanks for careing what we are looking for, and thanks for shareing what you ops are looking for. AND welcome to AS!!!!