I've just been dying for release to get some of these out, and even better: FD provided this handy suggestion forum. 
Most of these are simple things that really only require chaning UI elements to provide a bit more details to the player, but there are a few minor mechanical suggestions as well, and I will be sorting them into categories for easy reading.
FACTIONS
COMBAT
MISCELLANEOUS
Most of these are simple things that really only require chaning UI elements to provide a bit more details to the player, but there are a few minor mechanical suggestions as well, and I will be sorting them into categories for easy reading.
FACTIONS
- Ability to see faction-to-faction relationships. It would be nice to know who I'm going to anger if I work for someone else, as well as know who my friends and enemies are going to be.
- Better Influence Display. We can see a percentage of control in a system, but not the extent of a faction's control beyond a single system. When you look at a Faction's details, seeing all the systems/stations under their control would be perfect.
- In-System Space Territorial Display. A faction doesn't necessarily control all the space inside a system; sometimes the influence is split and you can be wanted/clean in a different area of a system than another. Seeing this in SC would be nice.
- Killing a faction's enemies should allow you to gain rep, and should not be counted as illegal by the faction you're assisting if they control that area of space. Even better if you could claim Combat Bonds for them, even if not inside a Conflict Zone.
- Faction "Quirk" Visibility. If any Factions have any special conditions about them that could affect your relationship with them (maybe they don't like Bounty Hunters in their space, for example), this needs to be relayed to the player.
- Do not display as hostile if not attacking and the faction is not hostile. If you attack a member of a faction, even if they are wanted, everyone of that faction who comes into the instance will display as red, even if they are not actually hostile.
COMBAT
- Personally, I would like if the weapons display would be reversed on the HUD. Currently what is on the left side corresponds to right-click and the right side corresponds to left. This seems odd.
- Display Bounty Value for In-System Wanteds. If a target has a bounty and is wanted in your current system (IE you can tell without a K-Scanner), display the bounty amount next to the "WANTED" status on the lower left target window.
- Display what subsystems are being targeted on the player's ship. In my experience, the AI knows what you're aiming at as they will constantly turn anything you select away from you; this can even be exploited a bit to get an AI ship to turn in a direction you wish. If the AI can see what subsystems are being targeted on them, why can't the player?
- Display a warning when a subsystem is close to destruction, and not just after.
- If you've successfully destroyed a ship, but that ship has not yet exploded, tell the player they've killed the target. Or just make the ship not take to long to explode. When multiple targets are shooting something or when you're expending expensive ammo, it kinda sucks when you can't quite tell if a guy is dead or just hanging on by a thread. It's even worse when you think you've got the kill, but it was stolen.
- "Match Target Speed" option for throttle. Honestly, Elite is the only space combat game I've ever played that has no such option.
- Auto-Field Maintenance Tools should be able to repair anything other than themselves (unless you have more than 1). It makes little sense that they can't repair critical ship systems, or even make inoperable systems operational.
- Allow additional ammo to be purchased and stored in Cargo Racks, similar to Hatch Breaker Limpets. Reloading from these containers should take a little bit longer and have the obvious effect of taking up cargo space.
MISCELLANEOUS
- "PIRATE," "TRADER," "CIVILIAN," "BOUNTY HUNTER," and "AUTHORITY VESSEL" kill missions could stand to be a little less vague. The most common thing I see with these both from other players and my own experiences is that what a player thinks is one thing, doesn't actually count. Ship types (Sidewinder, Type-6, etc) or factions could be used instead to target specific things for the missions. Unless this is a bug, and the obvious things should be counting, of course.
- Increased amount of hits to a target before an "assault" charge is issued or a way to ask for forgiveness. 1 stray shot when a police vessel cuts in front of you can seriously ruin your fun.
- More Player Stats/Information. Whatever happened to my total kill count? Why can't I see what upgrades I have on ships I am not currently sitting in? Anything I own or any stat that is tracked should be shown in the comprehensive player statistics window.
- In addition to the amount of a fine/bounty and the location it's issued from, a list of each transgression would also be nice. I really just want to be able to see a list of 500,000 counts of Loitering that makes me the most wanted man in the Galaxy.