A door that shakes and rattles when it's closed isn't resting firmly against its stop, the way it should be. For most interior doors these days, you can fix this problem by adjusting the latch plate that the door latch engages when shut. Find the little tab that sticks into the latch plate's hole, and use the tip of a screwdriver to bend that tab slightly toward the stop. Close the door. You'll know the tab is bent the right amount when the latch engages securely and the door doesn't rattle. If your latch plate has no tab, put some peel-and-stick silicone bumpers onto the side of the stop facing the door. They stop the rattling by pushing the door tighter against the plate.