If you run your Invoice A/R Aging report and an invoice shows that you know has been paid by the client, then the payment has not been fully applied to the invoice. The Invoice A/R Aging report requires that all payments/credit adjustments be applied to invoices in order to reflect them properly on the report.
A short cut would be to run the report, then click on the Invoice Number which will bring up the Invoice Details screen. From this screen, scroll down to the Payments tab on the invoice and click the Apply Payment button. If you already entered a payment or credit adjustment it will be listed in this window. Pull down the Payment drop down to choose the corresponding payment and click Save. If you have more than one payment to apply to this invoice then follow the steps again to apply all the payments out there and the Invoice will then be marked "Paid". Close the pop-up and refresh the report and the Invoice will no longer be listed.