[рони]

trio,
добавьте + в строки 9 и 12 (тут это 5 и 8)

(function(){
    var check = document.querySelectorAll('[type="checkbox"]');
    for (var z = 0, checkid; checkid = check[z]; z++) {
        if (localStorage[checkid.id] !== undefined) {
            checkid.checked = +localStorage[checkid.id];
        }
        checkid.onchange = function() {
            localStorage[this.id] = +this.checked;
        }
    }
})()