So take everything I say with a grain of salt pleases I don't know what is really planed by the Dev, and yes I did a search and found some things I am going to suggest but not all of them and not any ways to implement them, with my suggestions I will do my best to try and put a little info about how to implement them, or at lest die trying
and remember this is just my opinions, they are like #%^@@^@^@ 
everyone has one and they all stink.[Pretty sure this one is planed]
Shipyards, I'd love to be able to build my own ships!
Crew
So right now service crew do basically everything, what I'd love to see is more skills to be added like Gunnery that will improve the effectiveness of turrets and even fore facing weapons, Maintenance [see below] to improve the top end that the crew can keep the equipment maintained or reduces the time needed to make repairs or reduces the wear of equipment and such.
Maintenance or Engineering, right now crew doesn't really effect much at all but what I would love to see is your ships equipment deteriorate, I.E wear down and your crew has to maintain them other wise they lose effectiveness like shields not getting full cap or regeneration, may even randomly go down during combat or turrets stop firing if it gets bad enough.
[This would be done by a % where at X% so and so would happen but if it got lower then X% then more severe things would happen]
Training Facilities, I'd love to be able to build them at my HQ or even at my Stations to train my crew in things up to a point, like say 3 Star, Piloting, Management, Trade, Mining, Boarding Ect.
Equipment for our crew would be great! [and ways to make them] specially marines, Weapons would improve boarding strength, Armor would improve chances to survive if wounded and possible even use them medical supplies in a ship's med-bay to reduce or even care for injured marines that would of other wised died.
[also could add a new skill called medic that allows your marines to carry combat med kits to improve the chance of boarding or even just have medics to be hired.]
[Troop transport ships would be great as well.]
Supply, Simply put you'd make them at a factory, the parts used would be things like Hull Plates and such and they would be very cheap but to off set the cost of making them you'd make a large amount of them at once and you'd use them repair the ship out in space if they are in the ship's cargo hold.
Player HQ as it stands I don't like the way the PHQ looks, its just ugly to me, I'd love it if instead, the mission would just give you a Alien Power Core that you need to have in order to build the PHQ your self and then you could pick from some pre-sets.
PHQ
If the option above isn't suitable then maybe the option to pick where your PHQ is, instead of having just one anomaly you have one in each system or multiple systems and you can pick which one you want.
Another thing that would be cool is to have more military modals for stations, like gun platforms, missile bays and such so that we can use them as defensive platforms to defend sectors or gates and lanes.
Station storage management, basically having a cap on how much of a product you can produce and then stop before starting again.