Since it's looking likely an HD will be coming out in the next couple of years following the news of Shenmue III, what do you want to see in a HD release?
Personally I hope they demolish the loading times. I want to wait maybe one second, just enough to see the time flash up and the location, but that's it. I hated the loading times in the original, it kept killing the immersion.
They also need to fix the way he walks. It's too stiff and awkward with the d-pad - make it so he can move in all directions fluidly like many other modern games, and I will be very happy indeed.
Oh, and Japanese voice overs with English subs as an option please! It's so bad in Shenmue II with English voice overs that it absolutely killed the immersion. I hated it on the xbox. Yet on my dreamcast (european) I had the Japanese voice overs and it was perfect due to the excellent acting by comparison.