Also, slightly unrelated, but this for some reason reminded me of a certain issue some copiers had a while back, where they would swap certain numbers/letters for some reason when copying. Don't really remember what the cause of that was, though.
With simple technology, at first, you might get grainy or blurry images, or poor frequency response in audio. Those are easy to perceive as artifacts of the medium. Then you get things like JPEG fringes and context-dependent color shifts, which are a bit harder to learn to see past, since they are interacting with the image in sophisticated ways. JBIG (from the article) detects and compresses repeated textural elements or multiply-used glyphs, but if it applies that behavior to something that is actually information-bearing, it'll produce convincingly misleading artifacts.
There's a sequence in _A Fire upon the Deep_ where two people are conversing over a link with rapidly deteriorating bandwidth— their communicators are compressing more and more heavily to compensate, until at the end the character is "interacting" with a sophisticated Markov-like model of their interlocutor with only a few bits per second of actual entropy from the far end. Or possibly none at all.