Someone claims that HDMI has high amounts of jitter.

I can't say this makes sense to me. Unlike S/PDIF, HDMI seems to have a clock signal. It seems like a simple task for someone designing an HDMI receiver chip to correctly clock the audio.

Is there any solid evidence for or against HDMI having more than acceptable jitter? Doesn't HDMI require compliant designs to have acceptable jitter levels?

Well, the main test through which HDMI devices pass inspection is the eye pattern; sources have to generate a compliant eye, cables need not to worsen the eye by more than a certain amount, and a display needs to be capable of reading a signal which meets that eye spec. The eye pattern test will fail if there's more than about 0.5 Tbit of jitter between source and cable combined. So, compliance testing does test for jitter (and, in the case of displays, for ability to tolerate jitter) and if devices really are compliant, then no, there's not too much jitter for the signal to get through properly.

Kurt
Blue Jeans Cable (http://www.bluejeanscable.com/store/hdmi-cables/index.htm)