AJAX navigation breaks in 4.1

AJAX navigation breaks in 4.1

Hi.
I've got issues with navigation.
The site I'm building is almost entirely dynamically generated. Main component is a listview full of links, which build pages and proceed to them when clicked. On every page there is an anchor tag (in the header) that points to the listview page.
The HTML looks like that:

<div data-role="header">
  <a href="#contacts" class="icon-left" data-role="none"><img src="images/arrow_left.png" /></a>
</div>


It works only once. I mean, Only one click ever transfers user to the listview page. The rest is just ignored. It is like that since A4 (4.1 included). I could fall back to A3, but since I encountered a second navigation issue I feel like killing two birds with one shot.

Second issue:

I found working with JQM select widget a nightmare and since I don't need to send forms I built my own select widget. It's just an appearing div with some options. It is hidden and shown by .fadeToggle() method.
After it is shown and hidden the same button that didn't work earlier now forces whole page reload.
That's how I'm handling hiding this div and I feel it might be the reason of this behavior but I don't know how:

$(document).unbind('click').bind('click', function(e){
      if (selectMenuOpen) {
            $('.ui-select-protocol').fadeToggle('fast');
            $(document).unbind('click');
            selectMenuOpen = false;
      }
});







These two are probably separate issues, I had the first earlier, when this select-menu-replacement didn't exist. Also I've found similar threads in this forum and I've modified the library like the solved thread said, but it didn't work for me. 
I will GREATLY appreciate any help.
Thanks in advance.