I also want to add to the "mission"-action to have 1-2 more target possibilities. 1 damage can be used on Dieships e.g. to finish them off. But still, I'd like it to have a bit more tactical significance.
I too think that missions should have more options. Maybe you could steal or destroy artifacts. Same with leaders. The problem however is how to have a bunch of different mission options but keep the game simple enough to not have to look everything up.
What about a mission deck of cards? Each race gets so many Mission cards in hand, and can use the mission action to either discard and redraw or to perform on of the missions. The cards would give you a simple place to list all the details of the mission, and different cards could allow a variety of missions. (If you really want to customize things, each race could have separate missions, maybe somehow combine with Alliance cards?)
Further more, the Structure part of the Empire could have an effect on how many mission cards you can hold. I think there might be some real possibilities here. (Or maybe in the first expansion...)