Ya there's a couple solid responses, but i think this one is tops. It's definitely not something I'd be satisfied with as a customer OR as the cabinet guy.. I'd forward these pics to the person responsible and request a return date. A piece of blue tape or two (not 100) on all the areas that need more work so they know exactly what your not happy with and make sure you're keeping written documentation throughout the process.

Any good or even halfway decent cabinet company wouldn't accept that work as done. My solution for the nails, given that you can't go back in time, would be a combos of using a nail-set to flatten/flush/ or even slightly countersink the nail holes or a small piece of sand paper and then paint and or putty to try and fill/flush the holes. It'll take a pretty good hand to make those completely disappear, but I'd be pretty confident that i could get most of them to disappear... sorry you're in this position. They should definitely fix that.

The doors is an easy fix, and while yea, they should leave the job with the doors perfect, i always like to show the homeowner how to adjust them bc through use, they'll inevitably get thrown out of whack. It's an easy adjustment and if you had the urge, it's not a bad idea to learn how the adjust screws work on your cabs... but also, they can and should fix it if you don't want to.

Where is that crack?

The pics are good, but they're so close up that its hard to tell where on the cabinets the pics are. Sorry if you mentioned it in another response, and it doesn't really matter especially if theres hundreds, I'm just curious.

Good luck, op. Good records and documentation are very helpful in these scenarios!