Visual method. Sometimes a crack or hole can be found in a heat exchanger by looking visually with the naked eye. You may look into the heat exchanger cells with the burners in place or the burners removed. A much better view can be achieved with the burners removed. Remember, metal expands when it is heated. Of course when your furnace is running, it is in an expanded state. Any cracks in the heat exchanger will "open up" larger when heated. With that being the case, you would be more successful in discovering a bad heat exchanger when it is first heated with the burners up to operating temperature. Telescoping inspection mirrors can be used to view more surface areas. Some people like to purchase strips of scrap mirrors one inch wide by twenty inches long to slide into the cells. Even with mirrors, a technician's view will be extremely limited using this method.
Light method. Another way to view a heat exchanger is to slide a powerful light (long fluorescent trouble lights work well with this method) into each heat exchanger cell while looking through the plenum or blower opening. This, of course, requires the removal of the blower or an opening to be made in the plenum (preferably both) so that more heat exchanger surface area can be viewed. With the light illuminating the interior of each heat exchanger cell independently, visual observance of any light present will indicate a bad heat exchanger.