You can can hide the [Email] [Remind] and [Download] buttons in the full calendar event pop up window.

To do this you need to add a little code to the Admin Menu > Calendar Options > Expert tab 

Where is says "Web Tracking Analytics," copy and paste the following code into the blue text box:

<script>
$(function(){
  $('#popup_header').hide();
});
</script>

Save your calendar options screen.  Now, the area containing the buttons will be hidden from the pop up window.