I just had the same problem, I found that ClassName was NULL for one of the images uploaded I really can't guess on how this happened, I am reluctant to touch anything in the SS core so far I haven't had to, I fixed this by simply editing the record manually and adding Image (as it was an image) as the ClassName, hopefully doesn't happen again :)
I have the same problem: The class name in the file table is empty and the assets management is falling on a fatal error.
What I did:
I have a dataobject, which is in a many-to-many relationship to a page. The dataobjects are editable within a popup window in the cms. I added a standard image field to this popup. On selection of a file from the local filesystem, everything works fine. But if the image is added from the assets management, the classname field in the file table is set to null.