It depends on the type of distortion. Higher harmonic distortion is much more audible than lower order harmonic distortion. Supposedly odd order harmonic distortion is more offensive than even order harmonic distortion (kinda like the Star Trek movies), so third order, fifth order, etc ought to be something to look for, but, to be honest, I personally don't exactly know which distortion sounds like what. I do know that a sub with greater distortion is going to sound louder than a clean sub for the same output level on the same source material. Second order harmonic distortion is not easy to perceive, and is considered generally harmless, however I am sure that is only for the levels it is normally kept to in any decent subwoofer. I would guess something like 50 percent second harmonic distortion on a test tone would be pretty noticeable. By the way, I guess I should say at this point, in case you don't know, harmonic distortion are frequencies produced higher than the original fundamental frequency, so they should sound like a higher pitched addition to the original signal.
By the way, harmonic distortion at 20 hz ought to be very perceptible if you are playing a pure 20 hz tone. Since 20 hz is so difficult to hear as is, any other frequency produced by the sub should stick out like a sore thumb. However, in actual music, movies, and games, I am sure it would be far more difficult to discern distortion resultant from a 20 hz frequency playback. 50 hz should be a bit harder, but, of course, it depends on the distortion amount and distortion type.