ISSUE #1:
I tested and found you can not apply a badge with value of 0 (zero).
I can understand the original logic why - however it is problematic with dynamic updates of the value via jQuery. Instead of it disappearing it does nothing and leaves the old value.
<div id="foo" data-role="view">
<a data-role="button" data-badge="1" data-click="resetClicks">Reset Badge Count</a>
</div>
<script>
var app = new kendo.mobile.Application();
function resetClicks() {
this.badge(0); //set new badge value
}
</script>
You might consider adding another option flag: data-badge-showzeros to handle all possibilites of user needs. Some may want to show Zero values and other not.