After months of toil, strife, and seemingly endless backstage drama, the Christina Applegate-led revival of Sweet Charity has opened on Broadway. “This production has generated theater news of a kind you supposed didn’t happen anymore, or perhaps never really happened except in old backstage movies. Star breaks leg (well, a bone in her foot) twirling off lamppost onstage in Chicago; talented understudy (Charlotte d’Amboise) opens for star in Boston; producers decide to close show; star insists that she will, will get better in time for a delayed New York opening and helps raise the extra money to ensure show’s arrival, just before the deadline for Tony nominations.” But a fairy-tale ending requires more than determination, and Charity may not make the cut.