[javascript] Javascript: set label text

InnerHTML should be innerHTML:

document.getElementById('LblAboutMeCount').innerHTML = charsleft;

You should bind your checkLength function to your textarea with jQuery rather than calling it inline and rather intrusively:

$(document).ready(function() {
    $('textarea[name=text]').keypress(function(e) {
        checkLength($(this),512,$('#LblTextCount'));
    }).focus(function() {
        checkLength($(this),512,$('#LblTextCount'));
    });
});

You can neaten up checkLength by using more jQuery, and I wouldn't use 'object' as a formal parameter:

function checkLength(obj, maxlength, label) {
    charsleft = (maxlength - obj.val().length);
    // never allow to exceed the specified limit
    if( charsleft < 0 ) {
        obj.val(obj.val().substring(0, maxlength-1));
    }
    // I'm trying to set the value of charsleft into the label
    label.text(charsleft);
    $('#LblAboutMeCount').html(charsleft);
}

So if you apply the above, you can change your markup to:

<textarea name="text"></textarea>