Incorrect motion estimation data (e.g. datamoshing), Gibbs effect ringing, seams that come from JPEG-style macroblocks are all noticeable artifacts, along with noise from tape decks. They might not have started the genre, but they're certainly part of it now. I see nothing major to correct.
Pops and crackles to simulate vinyl record noise, too. Bands like The Bird and the Bee, and Death Cab for Cutie add those imperfections to digital tracks to get the sound they're looking for.
Thomas Ruff comes to mind as a prominent artist (photographer) working with JPEG artifacts.