Meteor jquery-ui slider integration
I think you can avoid the Tracker.autorun completely by updating the value in a template helper -- this is possible because your data is coming from a Collection, so it's already reactive.  You can play around with it in this MeteorPad, but a brief summary follows:

&lt;!--HTML--&gt;
&lt;template name="slider"&gt;
  &lt;div id="slider"&gt;&lt;/div&gt;
  Slider's current value is...{{sliderVal}}&lt;!-- You could get rid of this and just do {{sliderVal}} and have that return nothing if you want no text--&gt;
&lt;/template&gt;

//JS -- ommitted the rendered bit, which looks identical to yours w/o the Tracker.autorun
Template.slider.helpers({
  sliderVal:  function() { 
    var slider = Slider.findOne(); // this guy is reactive, so when another client updates the Collection, it'll get pushed to us
    if (slider) {           Template.instance().$('#slider').data('uiSlider').value(slider.slide); // Template.instance() b/c `this` doesn't return a template instance in a helper
      return slider.slide; // again, here you can return nothing if you'd rather have no text
    }
  }
});