Could be a script conflict, error in the world clock that's not visible, CSS override, etc. One thing you can try is opening the Developer toolbar in IE (press F12) and click the script tab, then click Start Debugging. That should reload your page and throw any script errors if there are any.
However, chances are it's a CSS issue, does the world clock have it's own CSS references? Is it overriding any OOTB SharePoint classes? Can you point us to the script?