I have a Harbor Breeze ceiling fan. Starting last week when I turn it on the body and light housing rotate about one inch of movement, there is a slight scraping sound until the fan gets up to speed. When I turn it off the body and light fixture reverse about one inch of movement. I have checked the blades and housing and everything seems tight. What do I do?

It's obviously the ceiling mount where it is attached to the ceiling that is coming loose. Would suggest you start looking there before it completely comes loose and crashes down to the floor.

If it is a threaded connection slipping, it may be missing the pin to keep from turning.

Usually besides the set screw, it has a Pin and a clip. Do you see a hole through housing perpendicular to set screw location, about a 1/2" up from set screw?

I agree. Check first that the ball of the downrod is firmly seated in the lip of the canopy/mounting bracket. Second, check that the downrod is firmly attached to the motor and all bolts, set screws, etc are tight. Third check that the downrod is firmly affixed to the ball. Lastly, check the mounting bracket and ceiling box.