This would be an error with PayPal, and I've seen a few reports of strange behavior at checkout today but nothing that suggests it is a wide scale problem affecting all PayPal users.
There's nothing we can do to correct or prevent PayPal errors on this end, but it sounds like the orders are being processed in our system since the buyer is getting emails from us with their order information.
If the problem persists please let us know, along with any other error messages that you hear about. If this continues we'll need that information to go to PayPal ourselves.