Hayabusa, obviously the first answer that you'll get is, "Well, GMAT itself means diddly-squat !!". But I think your question is deeper than that. Let me try to elaborate on your question (Please correct me if I am taking a different direction):
If one has fairly good experiences, great scores and good leadership skills, what can (s)he do to show that extra "spark" that H/S need (Without starting up companies, saving africa from starvation or finding the cure for cancer. How many MBA applicants have this kind of a background anyway?).
I read some posts by a girl (Intentionally not giving more details about her) who got selected in Stanford. Her sentence-formation and reasoning skills seemed quite ordinary to me (Although I do realize that people are not at their best when chatting on forums .. but I believe that your quality still shows). Without disrespecting her, I started wondering what kind of qualities she possessed that the school wanted her more than a lot of very strong profiles that we saw on GMATClub. I am not trying to diss her. I am just trying to find out in what areas I need to improve to be wanted by H/S.
ps. You may want to post this in the "The B-School Application" section also as a lot more applicants might have things to say and ask in this regard.