its hard to definitively draw a box around human hearing with easy to make and interpret signal measurements - hearing is complicated - which is different from the audiophile meme of hearing being "infinitely" more resolving than any measurement
for example there is "hearing below the noise floor" often cited - but that ignores full descriptions of "noise" - ignores our frequency discrimination that lets us hear other bands of low amplitude sounds even when there is a lot of noise in other frequency bands
a engineer would look at the human hearing noise floor in quiet over the whole range of hearing frequencies - and use that one strong limit on the ability to hear "errors" - harmonic, IMD, phase distortions of the waveforms that produce sounds below the limit
in each frequency band are certainly inaudible
its possible for some electronics to keep errors below that limit - but no sound transducers like speakers or headphones can when simultaneously creating enjoyably "loud" SPL as is experienced in even live acoustic music performance
but the human hearing threshold vs frequency in quiet curve is an extreme over bounding limit - clearly the existence of better perceptual lossy codecs like AAC, Vorbis which may only use 6-7 bits "mantissa" per critical band (the ~20% wide frequency bands which our hearing seems to use) argues that practical thresholds for many waveform error's audibility is about 1% in each critical band considered separately, allowing for logarithmic ranging
but if we consider intermodulation distortion products it is possible to construct 2-tone test signals that allow detecting a IMD difference product lower than -80 dB re the pure tones level with a wide enough separation of the test tones frequencies from the IMD distortion product frequency
however you can't point to any tonal musical instruments that even taken together can make waveforms with the properties of those test signals
there are some attempts to make relatively simple links between engineering properties of waveforms, distortion and hearing - Dr Geddes and his Wife have credentials, have done some tests -
http://www.gedlee.com/distortion_perception.htm
for electronics Geddes does propose hugely weighting low amplitude errors - you really, really don't want any crossover distortion in your amplifier output but he measured a number of cheap "chip amp" based consumer amps and found one of them did meet his low level distortion requirements - he has demoed his $4k? each speakers with a < $300 amp from Costco