I've been having this issue, and it's taken a while to try to figure out if it was an issue with the microprocessor or with my firmware.
That app note AN10974 is a good discovery. I think that information should be also in the errata for the processor, because it's a significant limitation of the processor that has caused me to spend some significant engineering time looking into it. I have the errata sheet ES_LPC176x, and item "ADC.3: Noise caused by nearby I/O pin switching activity or board design/layout could cause the ADC conversion results to be above the expected range." sounds potentially similar. However, in my case, I'm seeing glitches down to zero or towards zero, rather than glitches towards 0xFFF.
It seems to affect mostly AD0[3], on P0.26 (pin 6), which is right next to the SWCLK signal for JTAG on pin 5. To a lesser degree it affects AD0[2], on P0.25 (pin 7). However, if I put an oscilloscope on the pins, I see no visible glitches, so I guess cross-talk must be happening within the micro.