One strange difference in my opinion between Firefox and Internet Explorer and most strange of all also a difference to Google Chrome is that the onclick-event is not recnognized. Here is a simple example just to illustrate.
<option value="3" onclick="getCategories(3);">ACategoryWithCategoryNumberThree</option>
This works fine in Firefox, i.e. the function 'getCategories' gets called when choosing an object in the select box. This does not work for the other browsers though, the calls are not made and there are even no errors raised.
The solution is to make the function call on the select-tag instead using the onchange-event referencing the value of the select tag (which will hold the value of the chosen option-tag),
|<select id="category" onchange="getCategories(document.getElementById('category').value);">
This way it will work for all three browsers!