1) In-game cutscenes. Sometimes the mood of a situation can be greatly enhanced by going third-person to see something special going on. Too often, the player can be facing the wrong way, trying to line up a fighter when something important is happening.
2) The big, red, "You've been damaged!" effect.

Nearly every game has it anyway, so it always seems strange when playing a game that omits it. Barring use of a decent force-feedback system, it's also the best way to notify the player of damage, since most people pick up on visual information faster than audible notifications.
3) A decent sense of scale. I have yet to play a space sim that gets the scale right. I want to be able to fly nose-to-tail past a Deimos and be able to honestly say that it felt like I cruised about five-hundred meters. I want to ram an Ursa's top side and actually have it take up well more than my field of view, like it should. You get the point.
4) Planets. It'd be a new can of worms to open during development... You'd have to consider what fighters are capable of atmospheric flight, how to transition from space-flight to air combat, and most importantly, how planetary bombardment should look while the player's struggling to make escape velocity.

5) Branching campaign structure. Granted, each run through the campaign would probably be shorter, but it would be nice to have some say in who I fight for, whether or not I switch sides as I learn some of the backstory, etc. It also adds replay value, which is something FS2 would definately lack if it weren't for the great mission editor.
6) FRED3. Duh.
7) Shielded capital ships. It's the next obvious step. I think that the FS2 campaign, both for the Shivans and GTVA proved that bigger is not always better with capital ships. The next step shouldn't be another behemoth of a vessel, but a more technologically advanced vessel.
8) Bomber beams. Just another obvious tech advancement. Putting them on fighters might be overkill though... At the same time, it would probably be difficult to balance fighters and bombers if only one could carry beams... Let's just preemptively strike this one...
9) Specialized capships. While bigger ships are not always better, you could have individual ships that function as parts of larger capital ships. Imagine things like carriers, beam frigates, torpedo cruisers, and such. In general small battle group of specialized warships would be much more effective in combat than a juggernaut or two. (This is why present-day navies don't have an aircraft carrier-battleship hybrid.) It might even make the current idea of Destroyers in FreeSpace obsolete.
10) I'd like to write the plot, just to be sure it lives up to my expectations.

11) Barring another game (and I think it's safe to say that it's barred), a novel to cap off the plot would be nice. I think that a book would have one less copyright hurdle to overcome, and there would be significantly less time and expense involved in creating it. Probably still a "wishful thinking" idea though.