Why do many construction projects leave so many nails behind?
Yes it is typical, but a conscientious contractor will pick them up with a magnet or not let them drop to begin with. Sadly, from my experience, not many workers do. Cost of the nails versus the time needed to pick them up, it is cheaper to leave them. 

I would call and let the contractor know you are not content with the nails everywhere, see if any action is taken.