I know some of these ideas are probably already on here somewhere, but I'm pretty slow to acclimate to forum cultures and I find search tools a little bit hard to work with. Space on the internet being theoretically infinite, here we go:
1. Please add a dialogue box preventing the player from immediately switching on the transponder when doing so would alert a faction to the player's hostile actions. I did this a couple times in my first game in 7.1a, and, well, you can imagine that I felt a bit frustrated when I learned that "vengeful" is an impossible reputation status to get out of.
2. Turning Radius! This might not be a slight tweak or a small idea, but what about inertia? Specifically, in campaign mode (or whatever flying around star systems is called), there seems to be very little advantage to operating a fleet of small, light ships when fleeing from a fleet full of large, heavy ships, aside from certain terrain areas. If they can match your maximum burn, they can stay on you indefinitely, which is strange since I would intuitively expect heavy fleets to have wider turning radiuses than light ones. Honestly, it's kinda weird to be pursued by three or four hegemony patrols full of massive ships and being unable to shake them with a fleet consisting of a few frigates.
3. The ability to bribe the commanders of patrol fleets and, say, dockmasters or station commanders of otherwise hostile ports. Also, bribing in order to improve reputation with that faction.
4. A button to let the player orbit a planet passively, i.e. so one can take advantage of a planet's ring system to hide without having to periodically move one's fleet to keep up with the planet's orbital motion.
5. Let player fleets take shelter in space stations, or hide in the shadows of barren rocky moons, such that time can pass in the star system without the player being present or vulnerable to attack.