I apologize if some or all of these ideas have been posted already. At least the first one was discussed several times, I presume. But nevertheless, here is the list of suggestions.
1) Possibility of ship customization. Taking into account cutscenes, it cannot be as customized as Strongholds, but some degree would be quite good. Like collection of blasters in Hunter's ship, various trophies and so on.
And, perhaps, the companions won't just stand without movement. Maybe they can at least wander the ship or do something.
2) Talking about companions: I understand the reason why we cannot have full quests for all of them. And sometimes it has good IC reasons - as with Bastion attack and Sith Warrior. But if a character cannot participate... perhaps we'll be able to play as this companion for the time of the quest? Or just see the cutscenes - without playing the quest, but seeing our comrades in action.
3) Full IC chat. I mean - give an option to perform player-to-player conversation in the same form as NPC conversation - showing faces and movements, with dialogue window below, where you can type. I presume it will be RP-useful.
4) The option to summon... shadows of your other characters. They cannot really interact with anything, except the character you have actually logged in with, but they can be present and emote. That's why you can RP logging in with your Knight and bringing his Consular colleague to conversation, for example. Of course, it shouldn't work in instanced and PvP areas.
5) Perhaps there may be class-specific high-level quests for acquiring unique mounts for every class (we have almost class-specific ships, anyway). I admit that the first thing that came to my mind was "please, give Hunter a mission to acquire a Basilisk War Droid".