Ok, now for my opinion; I think whatever new direction Star Trek takes, it should COMPLETELY avoid Star Trek politics, because they're mostly contrived and follow an outdated policy. Give the people a coherent storyline, which is what everyone wants these days in their sci fi adventures: a big space opera plot that they can follow; the adventure of the week format is a little long in the tooth, and provides no area for character development. The biggest problem with Star Trek right now is that A) It's obsessed with technobabble, B) the starships don't feel like starships, and C) everything's too perfect.
How to fix:
A) STOP TALKING ABOUT IT. Technology isn't magic, it has limits. Star Trek writers should introduce a "tech cap" where they can't "modify the dylithium crystal matrix" to solve every problem that comes around. Giving people a limit to what they can do reintroduces tension. In TNG, that limit wasn't there, so you KNEW that they'd solve the problem with just a couple engine core tweaks.
B) Give us back bunks and heroic captains and laser battles. The thing that really made me feel that "wow...this isn't a starship, it's a pleasure liner with guns" was how the GUEST ROOMS in TNG were these giant three room apartments. I know it's the whole "city in space" idea, but you don't give every two crewmen a three room apartment. In TOS they slept in bunk beds in massive crew quarters, with bulkheads right next to them. You went "that's a starship, look, I can see the metal plating" not "thats a room with a view at downtown Chicago". I also want Captains that don't study Shakespear and learn seven different langauges in their spare time; I just don't relate to that. I know the whole "working to better themselves" mentality is at work in Picard's character, but please; we can't relate to wanting to study twenty times a day, or working without pay. Give us a captain that's heroic, but also human, where we can go "I want to be him". Also, give us space battles! I mean, they're starships! With guns! Blow something up for chrissakes!
C) Just STAY AWAY FROM THE ISSUE. Don't talk about it; introduce contradictions into it. My favorite new idea for a series is a Black Sheep type ship of the line, that's crewed with misfits and the like; it stays away from the "perfect universe" of usual Trek, but still GIVES us Trek.
Now, a lot of what I said may sound like TNG bashing; don't get me wrong, I really do like the ships and crews. I'm a TOS fanboy to be sure, but that's also because I like that TOS is much more real and down to Earth. They're both great series, it's just that TNG is what most people are basing their shows/games/whatever off of these days, so that's what I pick on most.