Taxonomy: taxonomies aren't output in preview
The taxonomy widget is unable to display the taxonomy links when previewing the widget. It will however display the title and label.
Preview:

Site:

Probably because it can't find the "current post" for which to display taxonomies. Can possibly get them using the post id of the page being edited, but that wouldn't work in the widgets interface for sidebars. Alternatively we can look at disabling the preview, or displaying all available taxonomies when there's no post id readily available.
A possible solution to this would be to disable the preview for this widget. This isn't a very visual widget so I doubt many people preview it.