Was giving Jack power in Golding's Lord of the Flies a mistake?

Giving Jack power was a mistake because it divided the boys from the beginning instead of uniting them, and did not give Jack any incentive to follow Ralph.
Ralph was elected leader because he was the one who blew the conch.  He found the special shell and blew it, and blowing it was what brought all of the boys together.  This and the fact that he was tall and dignified-looking was the reason that the boys voted him as their leader.

Jack started to protest but the clamor changed from the general wish for a chief to an election by acclaim of Ralph himself. None of the boys could have found good reason for this; what intelligence had been shown was traceable to Piggy while the most obvious leader was Jack. (Ch. 1) 

Jack is given the responsibility of leader of the hunters.  This means that there is division in the group from the beginning.  It also means that Jack has power.  He takes responsibility for leading the initial exploration of the island, knife in hand, because he feels like that falls under the responsibility of the hunters’ leader. 
A person like Jack should never have power.  Jack wants power in order to have power.  When the boys are creating their society, he is more interested in the fact that they get to punish people who break rules than the need for having rules in the first place.  Later, he ties a boy to a tree and has him beaten for apparently no reason.  Jack is a bully who likes power and violence for its own sake.
Like power being the more interesting part of leadership, Jack is more interested in the violence of hunting than the meat. The first time he sees a pig, he can't even stab it because he is so focused on the enormity of killing it.  Under Jack's leadership, pig hunting becomes more about war paint and a pig dance than the meat.

Then Maurice pretended to be the pig and ran squealing into the center, and the hunters, circling still, pretended to beat him. As they danced, they sang.“Kill the pig. Cut her throat. Bash her in.” (Ch. 4)

After the schism, most of the older boys side with Jack at first because he has the hunters, and the pig dances.  Jack's brutal leadership makes it impossible for any compromise.  His civilization is all about him. It's not about order.  It's a commitment to savagery.