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I just noticed that if you activate the module level caching for NewBB 2 that it breaks the drop down menu's. With module level caching enabled the drop down menu's are displayed in the same way as when you are using a theme without the <{$xoops_module_header}> tag in it. It looks as if something there is being cached that really needs to be executed on each page view.
Perhaps you could use the smarty insert tag as I did in my page execution timer and MySQL query counter smarty insert plugin so that whatever is handling the execution of the dropdown menu's is ALWAYS executed, and never cached regardless of module cache setting?
I have submitted this as a bug report
here.