jquery click event not firing?

Is this markup added to the DOM asynchronously? You will need to use live in that case:

NOTE: .live has been deprecated and removed in the latest versions of jQuery (for good reason). Please refer to the event delegation strategy below for usage and solution.

<script>
    $(document).ready(function(){
        $('.play_navigation a').live('click', function(){
            console.log("this is the click");
            return false;
        });
    });
</script>

The fact that you are able to re-run your script block and have it work tells me that for some reason the elements weren't available at the time of binding or the binding was removed at some point. If the elements weren't there at bind-time, you will need to use live (or event delegation, preferably). Otherwise, you need to check your code for something else that would be removing the binding.

Using jQuery 1.7 event delegation:

$(function () {

    $('.play_navigation').on('click', 'a', function (e) {
        console.log('this is the click');
        e.preventDefault();
    });

});

You can also delegate events up to the document if you feel that you would like to bind the event before the document is ready (note that this also causes jQuery to examine every click event to determine if the element matches the appropriate selector):

$(document).on('click', '.play_navigation a', function (e) {
    console.log('this is the click');
    e.preventDefault();
});

You need to prevent the default event (following the link), otherwise your link will load a new page:

    $(document).ready(function(){
        $('.play_navigation a').click(function(e){
            e.preventDefault();
            console.log("this is the click");
        });
    });

As pointed out in comments, if your link has no href, then it's not a link, use something else.

Not working? Your code is A MESS! and ready() events everywhere... clean it, put all your scripts in ONE ready event and then try again, it will very likely sort things out.