Headphones won't exactly show it at its best, as they are far too low impedance and will probably alter the characteristics of the output filter; I would suspect you'll also be overdriving the output buffers, which can definitely result in nasty artifacts due to the opamp going screwy.

Yes, the mk1 has some low-level background noise, but it's pretty quiet. It's so quiet as to be very hard to find on the mk2.

Hugo