The document node edit form is rather confusing, since it does not show the file when a file is already attached to the document. It only shows 'Select Document' with explanatory text that is a bit hard to understand.

[Select Document]
Document to upload. This document should only be specified either while creating a new node, or while creating a revision for an existing node. The document will not be saved while updating an existing node, if a new revision is not created for the node.

like filefield, just showing the uploaded filename (with document icon) would be best, I think.

And, the file display cannot be changed, since it does not show as field in the node display settings. Would be nice to be able to change the display of the attached file in the node view too.