We have a Excel 2003 document that is saved as a shared workbook which works for Excel 2003, however it it also used by Excel 2013, I don't think Excel 2013 is working properly with the shared workbook, it seems to save the document without the shared workbook setting. Is there a sharing option that will work with both Excel 2003 and Excel 2013?
Shared workbooks are dangerous. They will become corrupt, and once they show problems, they are impossible to troubleshoot. Excel was not designed for simultaneous multi-user editing. If you require that functionality, look for another tool. Excel is not the solution.
One way to aggravate the headaches caused by shared workbooks is to use them across different Excel versions. Skipping ten years of Excel releases and expecting the inherently faulty and error-prone shared workbook technology to work between 2003 and 2013 shows a very optimistic attitude, but it looks like reality has finally caught up with you.
Consider yourself lucky that your workbooks still have all their data (or do they?). Backup often. As an intermediate solution, get all users on the same version of Excel. Backup often.
Then start looking into a new approach. You can store the data in a database like Access or SQL. You can still design the input interface with Excel and you can also have a reporting interface in Excel. Just don't allow Excel to handle data that is simultaneously edited by multiple users.
You won't be happy. Backup often.