The driver reads the Xuartlite's status register more times (like here), but it does not process the error values (overrun, framing, parity) in it just in one place (at the end of the XUartLite_ReceiveBuffer function). And since the errors are "clear-on-read" type bits, there is no chance to get the errors using the drivers.
I have started a thread in this topic on Xilinx forum as well.