re: Pulled the trigger on a new construction home - tell me what I need to look out for

Absolutely get your own third party inspector. Find one with good reviews.

Contractors are contractors. They’re in it to make money. Some are great but even those can make mistakes or miss punch out items. An extremely through inspection will at least give you a baseline of what deficiencies their are with the property and you can choose if they’re minor enough to overlook or to have the contractor address.