‘Snagging’ is the building industry’s way of down-playing defects. A snag is a defect, plain and simple.
I think what level of inspection you decide to do depends on the certification that the building has already received: basic Building control approval, or has it got NHBC – or similar cover (insurance backed)?
If you, or a friend know what they are doing then it’s possible to download a checklist from the internet and do your own inspection. One of the most searching tests is to use your phone as a thermographic camera (download an app) and examine the walls and roof. This needs a decent temperature difference from inside to out, but will pick up any gaps in insulation, vapour barrier tears or mortar bridging of cavities. Similarly insulation defects on the roof, or poor sealing of eaves etc will be revealed.
Your builder will likely shit himself when you threaten this.