Wow- so long it made me put it in two messages!

Cockpit- Virtual cockpit, DEFINITELY. Nothing has a greater improvement on the fun of a dogfight, IMO. With the virtual cockpit, of course, a full 3D cockpit, preferably one that varied by ship type.
More on missiles/weapons: These should also be newtonian in nature. Missiles especially. They should accelerate throughout their flight, with their initial speed being the same as the firing ship. Primaries also should add the velocity of the ship firing them, and damage should vary depending on impact speed as well as type of weapon.
Systems and hull should DEFINITELY be seperated- it should be possible to attack a subsystem or turret without even touching the hull. Or even do nothing more than superficial damage that doesn't affect hull integrity OR any systems.
Beams should NOT be able to simply ignore shields. That would only be allowed for specially designed and extremely rare torpedoes, that in the context of the game would either have to be preprogrammed with the proper frequency or would only be able to work after the proper frequency was obtained through a long scanning process.
Full, to-scale stellar systems with seperate methods for inter-system and intra-system travel, a la IW2.
NegspectahDek's description of critical hits. Right on.

Let's get away from just hitpoints, if it's possible.
More complex radar systems: I don't think this is really necessary. OK, maybe a bit more interesting than it is in FS, put a range limit on it that varies with the size of the ship being tracked.
AI: How could I almost forget? Need much better. Not sure how, but it has to happen! FS2 AI, for example, is quite good at doing what it is told- and nothing else. Give them some Situational Awareness, for crying out loud! Let them see that the guy moving onto their tail deserves a response BEFORE he is putting missiles through them! Easier said than done, though.
Being able to get out of your ship: I don't think it's worth the extra effort. Being able to dock and switch ships? Maybe.
Voice comms: Not worth my processor power, IMO. Even less so my bandwidth!

HIGH MODDABILITY! Whatever the sim, there will be things to improve about it. Always. By making the game easy to add on to, gamers can make it into whatever they want. Best example in existence: Half life. People are STILL coding mods for that engine!
Multiplayer: In addition to the below, a good Coop system is imperative. Flying on the same ship could also prove a ton of fun.
And probably the most ambitious of all:
Instead of just a single player campaign and token multiplayer, support for massive Internet team warfare a la Warbirds. Two, three, or ten teams to an Arena, and multiple styles of play, including CTF and other games in addition to standard force-on-force play. This, of course, would also be mod-extendable. The force-on-force would be kind of the core game- each team in an arena(size limited, of course, just to keep the action fairly tight) with a full spread of fighters, bombers, and capships. Players could choose to be any of these, including gunners on someone else's corvette or bomber. Once they died, they would respawn, although larger ships would probably have extended respawn times, or at least a transit to the battle arena long enough to prevent them from dominating the game. Various variations would balance the game differently- one mode would have so many "points" per ship type and would require each team's points to be approximately even. Another would have pilots who do well in fighters, turrets, etc earn the option to command larger ones, if a slot is open on that team to allow such a ship.
There are virtually infinite possible ways to arrange such a thing, I have to admit, I haven't really thought through it completely myself. The hardest part would be attracting a player base. But hey, I can dream, can't I?

I think I'm done now.
