I have the same problem with my LPC11U68 based board, although only in a certain scenario. If I power up my board with the BOOT pin high (normal start mode) I do not have have this problem. However, if I power up with the BOOT pin low and interact with the built-in bootstrap loader I do have the problem. Worse, none of the above fixes make the problem go away. Basically, as soon as I clear then enable the USART0 interrupt the USART ISR gets stuck in a loop where the interrupt ID is 6 (character timeout) and nothing I do actually clears this interrupt so that the ISR will stop triggering. I too have used an o-scope to verify that the RX line is stable in the mark state. For debug, I decided to read the IIR, LSR, MSR, and RBR every time the ISR is vectored to, but even that won't clear this interrupt. Can anyone provide some guidance to help me resolve this?
P.S. I'm using the bootstrap loader interaction to allow my app to know which way it started (normal reset, or bootstrap loader interaction) to make my app act in a special way when started via the bootstrap loader (i.e., to enable manufacturing test mode). We use this technique on a variety of ARM Cortex M based boards, but this is the only one that has this behavior. It's also the first LPC11U68 board we've tried this on.