My thoughts on what I'd like to see in E4:
1. The ability to name the planets, moons and other bodies in each system that has been explored by you - naming the star system itself is up for debate.
2. Expanding frontier boundaries that grow as time in the game progresses and includes those systems that have been discovered on the edge of the frontier by you. It would be interesting to see new faciltities being built by the different companies and organisations in game as time moves on. New places will be popping up fairly often allowing more to explore as you continue to play the game.
3. Ability to construct facilities and space stations on or in orbit around planets/moons even asteroids for trading and manufacture of goods. The ability to own more than one ship at a time and to use them to automate trading with a crew onboard.
4. New space objects like nebulea, pulsars and black-holes (and a supermassive one at the heart of the galaxy

). Even a supernova on very rare occassions that may happen in some systems creating those black-holes or neutron stars etc.
5. Treasures/ artifacts that are hidden all over the galaxy, such as special ships and goods that can be used to modify your existing ship/s (new weapons, faster and longer distance engines etc). Some scripted missions that list the location or vicinity or where these treasures are located. Maybe the locations of such can be randomly generated with each new game.
6. Dynamic Milky Way background. As you travel around the galaxy and towards or away from the galactic core this can be represented here. One example for this could be that as you approach the core the blob at the centre of this background becomes larger and more detailed until you reach the exact centre. I think something similar was done in Homeworld ?.
Something tells me that the core should have many reasons to make the trip worthwhile such as many diamond or gold rich systems (since there are a lot of old and massive stars in the core, this makes sense). Maybe add the features of the inner-spiral and ring of nebulea in the region to make it more interesting for us astronomy fans. More supernova (4.) take place more often here so getting to those precious resources will be risky if they are located in a system with a collapsing star. The supermassive blackhole should be an interesting location to add a large swirling accretion disk (can use that for a fuel scooping challenge ?) and other graphical wonders. Maybe, just maybe this blackhole could be used in the game for some useful purpose such as a gateway to another galaxy or something - I'm sure the developers could come up with something great here. Could even be a plot device for a mission. . .
7. Tools (maybe in-game) to create new custom ship hulls that can be saved as a file to disk allowing a community of users to s*** creations but not allowing the use of them until you have your own shipyard or something.
8. Some sort of modding ability be added to the game for those that wish to create custom content - although not really essential since I get the feeling that E4 will be dynamic in a lot of its content.
9. Secondary support craft for your ship. It would be great to have smaller craft for other areas of the game, such as planetside, that are stored in your ships hanger. Shuttlecraft that can be used for escape procedures and to land small ground vehicles such as armoured cars that can even explore all seas and oceans on a planet as well as land. Maybe you could use them to deploy submersible mines to drill for oil and gas this way if necessary as well as traditional land mines. One advantage of this is that you could land your craft and drive to a deployed mine instead of having to fly and land close by for retrieval - although the Frontier/FE method should still be possible for those of us that like to do it the traditional way.
10. I know that has been discussed already, but I'd like to see some sort of Internet multiplayer option for online play with other real people that make use of the game files already installed on single-player installations but which can be added to or modified as client patches are released. Since everything is already on your system in terms of graphic content, the on-line downloads for multi-player play will be a lot smaller. I don't know how feasible this would be.
If you made it this far, then thanks for reading !
Rant over.