Can I just say that I fucking HATE this forum software that likes to eat your messages? I can't wait for the new forum that's apparently in the works. In the meantime, retyping from memory:
Awesome discussion, particularly the points about layering, and rhythm and texture vs melody.
One of the things that makes New Order so interesting to me is what they did wrong - in a conventional band, Hooky should have been the lead guitarist and Barney the funky drummer. Instead we get a guitarist with an amazing sense of timing and a bassist with an amazing sense of melody, and everything is upside-down and perfect at the same time.
Another factor is the synthesis between members. JD was a collective creative engine, and that seems to have continued with New Order (they've described it as a democracy). Each of the individual contributions is often very simple in isolation, but when you combine them you get the proverbial whole greater than the sum of its parts. Gillian doesn't get enough respect, in my opinion, but when she left the band it noticeably suffered (sorry Phil), and it's impossible to imagine New Order without Steve (another one who defies expectations - not only is the drummer the most technically proficient, he's also possibly the smartest member).
Their music has been described to me as simplistic, and maybe it is from a jazzhead's perspective, but so what - no one's ever done more with less, as far as I'm concerned.