As
@solderdude points out, noise is a major issue in measurements of headphone distortion as typically conducted. Most sites measuring headphones at present are for the most part simply showing the noise of their measurement environments for many of their headphone "distortion" measurements - a telltale sign of this is THD decreasing with output level (Tyll Hertsens' measurements were very prone to this, as are RTings'), as the fixed environmental noise obviously can't tell when the headphone gets louder.
There are ways around this - better noise insulation of the measurement system is one, although my personal favourite is to average a large number of sweeps together, which attenuates the (random) noise while leaving the distortion harmonics at their proper level. This technique is quite time-consuming (my default measurement routine takes about 1.5 hours to measure THD for two channels at two levels), but allows for peering more deeply into the noise floor than you could otherwise manage without investing in some serious noise reduction.
In general, headphone THD is poorly correlated with audible problems. Most headphone harmonic distortion behavior consists of strongly-masked low-order harmonics, and tends to occur at frequencies where distortion audibility is lower (that is, there aren't many headphones that tend to have a lot of harmonics around ear resonance, although they do exist).
Fielder's headphone distortion testing showed audibility thresholds which would leave even most rather flawed headphones' distortion components inaudible in most cases, even with pure tones. Music will leave such distortion even less audible, as there are many more masker tones.
Interestingly, the most audible case of headphone distortion I've documented wasn't by any means the highest in measured THD - it was with Focal's open-backed designs (Elex, Utopia, etc), which when driven to high levels (input voltage at or above what would be required for 105dB @ 1khz, which since Focal designs are bass boosted, translates to something around 108-110dB to my memory) and low frequency produced a "hard clipping" sort of distortion, with many
extremely high order harmonics (out into the mids, easily, for a 20hz sine wave stimulus). This was extremely audible, and has been subjectively noted on a number of forums.
Thus I'd tend to argue that unweighted THD verges on uselessness. Something like Earl Geddes' GedLee metric might be enough to make THD somewhat representative, but he didn't consider it all that useful to apply even to the higher-distortion case of speakers, so perhaps the conclusions it would bring are simply that harmonic distortion isn't a problem for headphones outside of rare cases.
I have seen some - including Christopher Struck of CJSLabs - call for more use of multitone tests of headphone distortion. I can see the theoretical support - my music certainly tends to have more than one sine wave, I don't know about you - but both theory and
the results of Steve Temme's test of headphone distortion audibility (which was something of an extreme case - the headphones were recorded playing at levels where masking would reduce distortion audibility more significantly, then played back more quietly) tend to incline me to think that
a coherence-based metric using music as a stimulus would be best in this regard. It's something I'm working on presently, but I have no meaningful data correlating to subjective perceptions yet.
In general, the preference test data we have about headphones from sources like Olive strongly indicates to me that distortion isn't a major concern for headphones, however - frequency response is overwhelmingly the largest factor in how headphones sound, and if that is wrong, no amount of zeros in your THD number will matter.
