Bind events directly to the input element. Use jQuery Mobile's virtual events, or bind standard JavaScript events, like change, focus, blur, etc.:
input
$( ".selector" ).bind( "change", function(event, ui) { ... });
The slider plugin has the following custom event:
create
$( ".selector" ).slider({ create: function(event, ui) { ... } });
slidestart
$( ".selector" ).on( 'slidestart', function( event ) { ... });
slidestop
$( ".selector" ).on( 'slidestop', function( event ) { ... });