As far as I am concerned, the most significant problem with the H2 (and one which puzzles me greatly) is that recording via the mic inputs is very noisy compared with the internal mics, which I'd rate as being commendably quiet for the price (and quantity!).
It's as though the mic input socket goes through a completely different preamp from the built in mics - but why??!
So, the most simple requirement would be that the external mic socket (complete with its provision of "plug in power" ) should be routed through the same quiet preamp as the built in mics, instead of the naff preamp it currently uses.
Maybe it's the plugin power requirement which meant that they had to use a different preamp route?
Access to two preamps would of course be even better, if a second mic input were added.
Line input is fine, though over-sensitive.