Zack's fatal mistake (although i dont really believe this) is being blinded by love.
He oughta runaway with Cloud to places faraway and never return. So that he could breath a new life and luxuriating over what freedom offers out there.
However, being a... (sorry Zack and Zack's fans! Hey i'm also his big-time fan..) dumbass as he is, he returned.
Returned to Midgar, the base of Shinra Corporation that was hunting him down, determining to terminate him from existence.
All because of a girl named Aerith.
That was the start of it all.