Congratulations on the new home! If concerned about the construction talk to an inspector and see if he will make you a package deal where he does a couple of walking inspections and a final one. And yes, I think it's a good idea. An experienced inspector can suggest better ways to do things here and there. True, it may cost you more money up front if you want to change something, but I believe it's worth it in the long term. Not to mention a little peace o' mind.
I agree with brianl703 in that most problems don't manifest themselves until long after a builder has forgotten your name (and how to use a phone to call you back.)
My neighborhood is 10-13 years old and I've seen a disgustingly large amount of repair work going on. HVAC replacements, new roofs, water heaters, appliances, screen/storm doors, vinyl siding failures, etc.
In fact, I'm in the midst of replacing the nails in the kitchen floor with construction screws. The crew that installed the sub-floor missed the joist with about every other nail and used smooth shank nails. Should have been ring nails. So I ended up with an unbelievably noisy floor. Squeaks and pops everywhere all the time. And as we replace the carpets, I will be replacing every nail I can get to. And what's worse? Same crew apparently put the OSB on the roof, again missing the trusses with about 1/2 of the nails. There are a few hurricane straps visible but when the wind blows strongly I get a little nervous...