Yes, I would have to agree that interaction with the environment would make the game a lot more enjoyable.
My pet hate is coming across lots of doors and windows that don't break and don't open. This was one of the things that really annoyed me about Heretic II, to be honest (especially after Hexen and Hexen II had featured breakable glass). I'm glad to see the glass is back in for JKII.
As for the rest of the environment, I too would like to see more interaction with the environment. In Dark Forces, for example, you were given the opportunity to crack some Imperial codes. It was a very simple system which worked well, IMO.
Perhaps we could have some similar features in JKII. A little bit of data slicing, for example. Or being able to play back holo-recordings in real-time. Maybe get an R2 unit to jack in and unlock a door for you.
As for crates - well, I'd want the same kind of destructability as those in Half-Life. I mean, unless it's specially shielded, it shouldn't be impervious to a lightsaber.
Driveable vehicles...yes, of course, which is why I started a thread on it elsewhere.
Even the ability to turn lights on and off - and that was also somewhat used in DF, on the level where you had to turn the power on.
What I'd also like to be able to do, which I think has been mentioned before, is sit down and play that chess-type game on the Millennium Falcon.
In addition, it would be really great to be able to join a table of tough-looking aliens, and join in a game of Sabacc.
Or just sit and watch a proper Jizz band playing.
Of course, including a lot more furniture than JK had (destructible of course) would be good. And maybe have a Stormtrooper locker room, where you can search through their lockers for equipment - or even to disguise yourself as a Stormtrooper...
The possibilities are endless. Unfortunately, their budget isn't.