Ajax error on saving multi-valued file fields

I have discovered that if a node has a multi-valued file field (one where more than one occurrence is permitted), then an attempt to save one or more files to that field will result in an ajax error as follows:

An AJAX HTTP request terminated abnormally.
Debugging information follows.
Path: /system/ajax
StatusText: n/a
ResponseText: 
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Error
Error message   Notice: Trying to get property of non-object in file_field_presave() (line 220 of /home/james/vmg-apws/modules/file/file.field.inc).  Warning: Creating default object from empty value in file_field_presave() (line 221 of /home/james/vmg-apws/modules/file/file.field.inc).  Notice: Undefined property: stdClass::$uri in file_save() (line 566 of /home/james/vmg-apws/includes/file.inc).  PDOException: SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry '' for key 'uri': INSERT INTO {file_managed} (filesize, status, timestamp) VALUES (:db_insert_placeholder_0, :db_insert_placeholder_1, :db_insert_placeholder_2); Array
(
[:db_insert_placeholder_0] => 0
[:db_insert_placeholder_1] => 1
[:db_insert_placeholder_2] => 1385000089
)
in drupal_write_record() (line 7166 of /home/james/vmg-apws/includes/common.inc).       
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ReadyState: undefined

This is caused by an entry in the list of file field values in the %form_state['values'] array returned to the submit function containing an entry for an "extra" file (presumably the input field that was empty when the save button was clicked) that has a fid of zero (see below for dump of 'values' array

Array
(
    [nid] => 91
    [vid] => 275
    [type] => apws_job
    [field_apws_work_files] => Array
        (
            [und] => Array
                (
                    [0] => Array
                        (
                            [fid] => 2084
                            [display] => 1
                            [_weight] => 0
                            [description] => 
                            [upload_button] => Upload
                            [remove_button] => Remove
                            [upload] => 
                        )

                    [1] => Array
                        (
                            [_weight] => 1
                            [fid] => 0
                            [display] => 1
                            [description] => 
                            [upload_button] => Upload
                            [remove_button] => Remove
                            [upload] => 
                        )

                )

        )

    [submit] => Save
    [form_build_id] => form-uHfm81xhCvehsQcvEIG6ZgXmEUwgwSWzXYsL1Ko9mRs
    [form_token] => xM-mQ4He4C_s_d0oafeWQh33O5GxoLtIX9-IIOxDV80
    [form_id] => editablefields_form__node__91__275__field_apws_work_files
    [submit-] => Save
)

This does not happen when the normal node editing form is used, even though this dummy entry is present in the $_POST array, so presumably the logic that builds the $form_state array in that case has filtered this entry out. I'm not sure where that happens, or what filtering is done.

I have not tested whether this problem affects other multi-valued fields, perhaps in a less catastrophic manner, so it might be more than just file fields that need to be looked at.