I'm having the same issue.  The behavior is not normal given that the "Browse" button does NOTHING at all when clicked even after the page fully loads.

 

What I found is that if I disable the Silverlight plug-in, the "Browse" button works.  I have:

 

Firefox 3.6.4 (but it happens in 3.6.3 as well)

Silverlight Plug-in 4.0.50524.0