I was thinking that stars should have specials - like planets - which would affect the whole system or the star itself.
Also I think it might be a good idea to bring in binary star systems as in where a solar system contains two stars. This could also lead to a special bonus for the system for things like solar orbital generators. For instance i think its blue or white stars that give the largest bonus but a binary pair of two white stars could give double the bonus or a pair or red stars could give the equivalent of a blue stars bonus.
One special could be a binary star. If the stars are orbiting close together all the plants would orbit around both stars (around their centre of mass). This would make it easy to add this to the game, as all that would be needed is a different picture for the star - in combat and on the planets sidebar. On the galactic map a single star image would still be ok as from a distance it would look like a single star.
A supermassive blackhole in the centre of the galaxy could just require a certain engine speed to allow travel past it. Other ships should just get a message that it is too dangerous to travel there (since someone who can fly a spaceship must know about blackholes!).
Binary star systems with stars far apart would involve planets orbiting each indivdual star - which would need a big change to the planets sidebar.
I think that in the game background something should be said about how stars with starlanes are rare. Only 10-500 stars in the galaxy have them. All the other stars would be useless to glactic empires as the travel times between them would be enormously long. Binary stars could destabilise the starlines - hence all the star systems in the game are (currently) single, when in real life more than half of stars are in binary systems.