Is there a Report That Shows Partially Paid Invoices?

There is not a report in the system that will show you partially paid invoices.  If you have a client-matter and invoice in mind, you can call up the client-matter in Matter Status.  Access the AR Ledger tab and then sort by the Reference column.  This lists everything in order by Invoice Number and shows the payments specifically applied to each invoice. Any invoice where there is an amount due AND there is a payment listed directly underneath it has been partially paid.