I think the main concern for me is that I do not want the game to fall to modern conventions which would detract from the experience. Sandbox games are a very big part of modern gaming, many seem to be jumping on the band wagon and the more that don't get slapped with the notion of being linear. But Shenmue has never been Sandbox. It's not just a static world which you play about in. Shenmue's Calendar System (Not sure what the proper term is) is what really sets it apart. Having the game take place over a set time period with days that go on and having the environment react to this progression of time - Like how in Shenmue 1 in the town you'd see the spirit of Christmas appear with the Snow & even a walking Santa! It's truly a world you feel apart of rather than just an open environment which you're more in control of, It's this balance which I hope they still perfect in Shenmue III.
Other things, QTE's. I know our generation has become tired of them but they're a staple in Shenmue and one I want to see continue. I like the Arcade vibe they bring when actions sequences heat up.
To be honest, I am not to concerned wit the games narrative, I mean this is content which has all been scripted for many years, I am confident it will be in the same spirit as the previous two games.
One thing I am curious about is the graphics. I have always said for years I would be content with a Shenmue III which is built on the same engine as 1 & 2... however, I don't know how I would react to something even better. I mean I don't view the e3 trailer as anything near final, but they looked a bit off still, I hope this isn't a feeling I still have upon seeing the final build.