CRM allows you to change the display fields used in an Search Select Advanced (SSA) field but it does not give you control over the order of the fields displayed.

The following function, placed in the custom content of the screen, will allow you to change the order of the display fields:

<script>
function ChangePopUpFields(fieldname, fieldlist) {
    if (window['NavUrl' + fieldname]) {
        var s = window['NavUrl' + fieldname].toString();
        s = s.slice(0, s.search('ViewField=')) + 'ViewField=,' + fieldlist + ',' + s.slice(s.search('&JumpReturnCol')-1);
        s = s.slice(s.search('{')+1).replace(/\}$/,'').replace(/"/g, '\"').replace(/\r|\n|\r\n/g, '');
  eval('window.NavUrl'+fieldname+'=function NavUrl' + fieldname + '(ID,url,fieldname){'+s+'};');
    }
}

window.attachEvent('onload', function () {
    // change the following line to have the field you wish to change, and the field list you desire
    ChangePopUpFields('oppo_primarypersonid', 'Addr_Address1,Addr_Address2,Addr_Address3,Addr_Address4');
});
</script>

It also lets you change the fields used in the SSA field dynamically.  For example, say you wanted to reverse the field order after the oppo_primarycompanyid field was modified.  To do this you would put the following code into the OnChangeScript:

ChangePopUpFields('oppo_primarypersonid', 'Addr_Address4,Addr_Address3,Addr_Address2,Addr_Address1');