For anyone else arriving at this question:
I was performing the most simple jQuery, trying to hide an element:
('#fileselection').hide();
and I was getting the same type of error, "Uncaught TypeError: Object #fileselection has no method 'hide'
Of course, now it is obvious, but I just left off the jQuery indicator '$'. The code should have been:
$('#fileselection').hide();
This fixes the no-brainer problem. I hope this helps someone save a few minutes debugging!