Richard,
The date of each payment application is recorded (table ARDetail) so it is possible to report on those invoices that are zero balance and the latest payment application date is within your report date range. If all invoices are created with an outstanding balance then the final payment date is determined in this way. If you also have fully paid invoices as of the invoice date (i.e.,, payments on orders or invoices), you will need to take that into account.