I let the bird fly all over the house but I pay attention to him: if he is in a grumpy mood he might chew on something he shouldn't. If he does behave badly, he likes witnesses to his transgressions.
He does not fly that often because he does crash occasionally and doesn't like that, but when he is zooming through the house at high speed he is impressive. He often prefers to grip my hand with his feet and 'fly in place.'
As for bird-proofing your house, unfortunately you really can't. Parrots chew through soft woods (e.g. pine trim) quickly. In my case, I only allow my bird free flight in certain parts of the house. I've put clear plastic bumpers--the kind of thing you can put on wall corners--which prevents her from destroying the trim on my door jambs. In other cases, e.g. the trim around my bathroom mirror, I've just given up.
Also, keep in mind that parrots are burrowing creatures, so if you give them other stuff to burrow into (aka chew/destroy), then they won't destroy your house as much. My parrot burrows into cardboard boxes that I give her. Think of it like providing a scratching post for a cat.
Also how did you birdproof your house so he can fly around freely?