How should I fix a large mirror ball with many cracked mirrors?
See if you can find some adhesive vinyl with a mirrored surface.  I had some a few years ago and it was every bit as reflective as the individual squares of a mirror ball.  The material is meant for use in a cricut or silhouette brand vinyl cutter and is probably sold at your local art supply store.
Cut the vinyl into squares the size of cracked mirror squares then peel off its wax paper backing and stick it over the cracked squares.