I'm having issues with SharePoint 2013 not saving due to required fields. I recently updated the lists with KWiz Field Grouping and removed the requirement of the fields to be completed. When I go check the options for the fields it says must be completed before saving, "optional" is selected not "required." The little asterisk is not there when completing the form but it won't save. An error message pops up stating that the fields are required and must be completed before saving.
Are you sure there is not a Required field missing (hidden) from your form?
Are content types enabled on your list? To check go to List Settings>Content Types>select a content type>check the Status column for hidden fields.