Not sure what's going on here. Inspecting code for a date field show's right markup (I think), but the date picker doesn't appear on profile date fields on frontend. In backend admin view of profiles, the date picker does appear.
The URL to the page is: http://www.cahpi.ca/demodate , and files in question have "Date" in their label.
I'm using a custom template (which is what you'll see at the above URL), but even when I use the default Beez3 template for Joomla, the date picker icon doesn't appear in the date fields.
I have multilingual civiCRM (English/French), but don't see that this would prevent date picker from appearing.