It's only recently that I've found any measurement to be very useful.  The Headroom FR + square wave + distortion graphs were cool, but didn't correlate that well to my experience with a headphone- they could measure really well and sound terrible, and vice versa.  Marv's CSD's are the first measurements I've ever found useful as an indication of how I will like a headphone.  Which may be because they are measuring the aspect of a headphone's performance that I'm most concerned with, and which is most often very problematic.  They've actually provided solid proof of why I've been so frustrated trying to find decent sounding headphones, and why I've had such an easy time finding a decent pair of speakers (only ever bought one pair of speakers in my life, and I've gone through probably a hundred headphones) It still isn't perfect whether it's the measurements, or more likely my ability to read them I'm not sure.  I have noticed that I can be quite confident in knowing that I won't like a headphone based on serious resonance problems in these CSD's, but headphones that measure pretty well are more ambiguous to me.  Though I'm getting better at combining FR with the CSD's to know better.  The HD800 is a good example because it's really clean but has FR issues that bug me.  I've learned things like a dip in the lower mids/upper bass seems to wind up sounding bad to me- cold or lacking warmth/body.  While dips in the upper mids aren't necessarily a bad thing for me.  And jagged FR in the treble or upper mids isn't a good sign even if it's not elevated.  etc... 

I have no idea how to read distortion graphs, but have no reason to at this point.  There are so few headphones that have clean response in terms of resonances, that it's pretty easy to just listen to them myself.  It's only a small handful, most of which I've heard already.

On the topic of measurements, what's the significance of phase response measurements? How do we interpret them?

That is a very good question. JA makes a mention of it here:

http://www.stereophile.com/content/thiel-cs5-loudspeaker-measurements-part-2
http://www.stereophile.com/content/thiel-cs6-loudspeaker-measurements-part-3

Also, what would happen if the phase of the left driver is different from the one in the right driver?

I know there are some all pass filters whose job is to affect the phase:

https://ccrma.stanford.edu/~jos/pasp/Allpass_Filters.html
http://www.prosoundweb.com/article/demystifying_and_overlooked_tool_using_all_pass_filters_to_improve_directiv/

Imaging as well I'd suspect.

I can see 2, 3, and 4 way IEM having to overcome phase issues due to the cross overs.

How about the bast majority of single driver headphones? My only guess is that phase issues may happen due to internal reflections in the cups (dampening and stuff). Phase issues may be worse here since reflections can introduce standing waves producing large peaks and suck outs. Ultrasone would be an interesting study can given it's amazing 3 tap impulse response (two reflections even coming at 180 degrees!)