Digital interconnects generally do not have error correction. Signal degradation with digital interconnects generally shows a cliff effect, but it's a myth that you get either a perfect picture or no picture. At some point the receiver loses lock, but before that you get a gradual escalation in bit errors that may or may not be obvious: http://www.audioquest.com/resource_tools/downloads/whitepape... (see page 6).

And with audio, errors caused by digital transmission, mainly clock jitter, can be quite subtle: introducing low-amplitude unwanted signals into the analog reconstruction.

I'm well aware that there are intermediate states between perfect and no picture. My point is that the errors are always going to be obvious, not that they'll destroy everything. If any errors at all are happening on your HDMI cable, you'll see obvious errors in the picture. If errors are happening in a digital audio cable, you'll hear obvious errors in the sound. If you can't hear or see any errors, then there aren't any. Not every error will produce a discernible visual or audio artifact, but if they're happening with any regularity, then you'll occasionally get one in a high-order bit instead of a low-order bit that will make its presence obvious. It's not possible for the errors to only show up in the low-order bits.

Clock jitter is an interesting point, but I can't see how the effect could possibly be perceptible, given that the clock in question is running at an order of magnitude or two faster than the audio sample rate, and any jitter in the signal due to the physical cable will be orders of magnitude smaller than that. Those "low-amplitude unwanted signals" would surely be in the megahertz range, far beyond any possible human perception.