From the "well, that was a no-brainer" department…
From the Settings screen, click Document Settings, and then click the Invoice tab. You'll see a new option under Payments:
Check this box (and don't forget to click the Update document settings button!) and you will no longer have to explicitly mark an invoice as paid once it has a payment and its balance is zero; it'll get marked paid automatically. This will happen whether the payment is an online credit card payment, is logged manually, or is added from QuickBooks™ or Xero and then synced to Kickserv. Note: this will not affect any existing invoices--only ones that you create from this point on.
We know, we really should have done this long ago. Hope it's worth the wait!