I plan to snag my own apartment when the time comes. Most people can spot a good job from a bad one, especially if your in an empty room. My background is Shopfitting/Joinery and I don't imagine there will be to many snagging issues to worry about. My only question would be how you check plumbing and electrics if it's possible that these are not connected when you snag it.
That said, the main things to look out for are any moving parts (doors, shutters, windows,plumbing and general fitting quality). Here's a small list of what I'd be looking out for.
1) Hot water is working ok
2) no leaks from plumbing in kitchen & bathroom
3) Main door & patio doors work smoothly and lock easily
4) All internal doors open and close smoothly including locating securely into keepers
5) All security shutters, manual & electric, work smoothly
6) All kitchen doors and drawers are hanging level, handles secure
7) Kitchen Sink & Tap secure
8) Kitchen worktop sealed around walls
9) Bathroom bath panel secure
10) Toilet seat secure
11) Bedroom wardrobe doors run smoothly
12) Windows open and secure easily
13)General good quality fitting of all items
Midge