I'm an installer for a custom cabinet shop. We run a LOT of crown, base trim, cove, etc. So, a few things on at least the wood working stuff.
Go around and and put a little piece of painters tape on every nail hole that they missed. Actually, go around and put a little piece of tape on every "ding" everywhere you see them. Make the contractor fix them. The painters should probably be some of the last guys in the house before you move in. They touch up any paint and trim dings/scuffs to make it look all new for you.
We use a couple different types of filler to hide all sorts of blemishes in our cabinets and trim. The little Minwax cans you can get at Menard's or Home Depot are generally pretty good for small holes. (I've never seen the full assortment of colors in any store. I can't find teakwood, redwood, or briarwood ANYWHERE.) That stuff is quick and easy. It's best on the lighter colors of wood and gets tough to match darker stains on oak/lyptus/cherry. Hit it with some stain if it doesn't match.
We also have these:
Wax sticks
Stain markers
Graining pens
I've been able to fill counter-sunk screw head holes in plain sight with that set. We're talking next to a customer's dishwasher, hip height, full sunlight and I couldn't see it from three feet away. (It can take a lot of time, but that time spent is generally better than me having to call my boss to order a new cabinet.) It's probably way overkill for you, but know that it exists in case you ever have some trim damage that you'd like to fix.
Know that the guys are going to be pissed when you tell them about the nail holes they missed. If you don't putty holes as you make them, it's a shitty job to rework and easy to miss holes. They know it should have been done right the first time and will be frustrated at themselves for it, but probably focus that frustration on you.
Just some info and perspective from a trim/finish/cabinet guy.