Changing calling javascript function variable with jquery?

The way to do this with jQuery is to move all of the Javascript code into a separate file or script block within the HTML. Any way which abstracts the display (HTML + CSS) from the behavior (Javascript)

This will require a bit of reworking of the HTML. In particular removing the duplicate id fields in favor of having id's be unique. Additionally removing the javascript references from the onclick handler.

<div id="list1"><a>+</a></div>
<div id="list2"><a>+</a></div>
<div id="list3"><a>+</a></div> 

Then with jQuery you can specify the behavior of these links directly from the JavaScript. This is true for both the play list links and the one which modifies them to pass '2',

$(document).ready(function () { 

  var secondArg = '1';

  $('#list1 a').click(function (e) { 
    addplaylist('shv231a1', secondArg);
    e.preventDefault();  // Don't follow link
  });

  $('#list2 a').click(function (e) { 
    addplaylist('jhr2a13', secondArg);
    e.preventDefault();  // Don't follow link
  });

  $('#list3 a').click(function (e) { 
    addplaylist('thy2b1k', secondArg);
    e.preventDefault();  // Don't follow link
  });

  $('#make2').click(function (e) {
    secondArg = '2';
    e.preventDefault();
  });

});

This is a possible solution:

<a id="make2" onclick="javascript:changeToTwo();" href="javascript:void(0);">Change the value 2</a>

Javascript

function changeToTwo() {
    $('div#list a').each(function() {
        $(this).attr('onclick', $(this).attr('onclick').replace("'1'","'2'"));
    });
}

If I remember right ie will only select 1 element with the same id so you may want to consider moving it to a class selector

1) Ids should be unique on a page 2) use a class to select 3) keep your functional code out of the markup

HTML:

<div id="1" class="list"><a>+</a></div>
<div id="2" class="list"><a>+</a></div>
<div id="3" class="list"><a>+</a></div>

javascript:

$('.list').each(function ( index, element) {
    addplaylist(element.id);
});