I've been compiling notes on needed interface, UI, graphic, and quality of life improvements.  I'll update this OP as I have other suggestions (and/or will add other's suggestions to it if I agree!).  Here we go:

Galaxy / Strategic View

1. EXPLORED AREA: Very difficult to tell easily where you have already explored, for example with probes.  I've had games where I have not been able to find a way out my constellation easily because there was star system hidden in a small little area that I missed because it's so hard to tell at a glance what is explored or not.  Maybe even have a map-mode toggle to show as an overlay what is currently explored.
2. SYSTEM & PLANET LIST: Add a menu or side panel that lists all explored systems with the types of planets and their resource levels.  Will help with growth / expansion planning.
3. PLANET MOUSE-OVERS: The little dots / circles for planets when zoomed out - mousing over them should list the type of planet it is.  It will make it much easier to see what colonization tech you might want.
4. END TURN hotkey: yes - add one!
5. BUILD QUEUE QUICK ACCESS: Clicking on the build icon n a system from the galaxy view could (should) open up a panel with the build queue.  Would make it a snap to manage systems right from the map instead of diving down to the system level.
6. OVER-COLONIZATION: Need an indicator somewhere for the colonization limit and what the penalty is.  Make this prominent! 

System Management Screen

1. Controlled System List: The system list needs to be its own button at the top of the UI bar.  Having to go through a different UI menu each time you want to view it is irritating.
2. List of Built Improvements - Built improvements should be a separate TAB in build queue instead of its own separate screen.  Usually if you looking at the list of existing improvements, you want to also be looking at the rest of the system screen in order to make a decision (where to put population, what the economic upkeep cost is etc.).  Plus the button to find it currently is hard to find at first.
3. Toggle / Force Expanded Build Item List: I'm getting tired of constantly expanding the build queue - make a settings option to just toggle the expanded panel on/off.

Population / Migration

1. MOVE POPULATION - We should have a way of moving population (even if it makes that population unhappy in the process).  Maybe when all the migration mechanics are worked out?
2. MIGRATION BUGS - I think this is a known issue that foreign population from factions/minors you haven't met yet and that aren't part of your empire will migrate onto your worlds. That's really strange.

Fleet Movement & Management

1. FLEET MOVEMENT INDICATOR: When you select a fleet and start moving the mouse around to different systems/starlanes, it should immediately start drawing + showing you the movement path the ships will take with the indicators for how far the fleet will go each turn.  it is freaking SO ANNOYING that you have to issue the movement order first to see the distances it will move. 
2. MOVEMENT MIS-CLICKS: I found myself accidentally moving fleets a lot.  There needs to be a key (e.g. ESC) that will de-select a fleet if you have one selected. Or have movement require a double click.  Or even better, when you assign a fleet order have it "locked in" but don't execute it until you press the "move fleet" button (or double click to advance that fleet).
3. MOVE FLEET HOTKEY: A hotkey for the move fleets button would be nice.
4. LEADER SHIP HEALING: Using the "heal fleet" button doesn't heal a leader's ship if a leader is assigned to that fleet.  I've only been able to heal a leader by modifying their ship design and paying the upgrade cost in the process.
5. FLEET HEALING: This is more a design issue - but fleet that are garrisoned should slowly heal over-time (5-10% a turn would be reasonable).  Just to give an option to a player in financial trouble.  Thematically, the upkeep cost for ships would include the need for repairs over time. 
6. SELECTING/DE-SELECTING MULTIPLE FLEETS - Clicking on a fleet should select/de-select that specific fleet without affecting others already selected so that you do not have to hold CTRL (or SHIFT) to select multiple fleets.  This would make fleet management function on a touch screen (and be more intuitive for many people regardless of the touch screen).

Special Screens & Overlays

1. ECONOMIC SCAN SCREEN: This looks cool but is not very useful.  I would show the total resource output for all resource types as a small info box next to the systems.  The fuzzy cells look nice but don't convey the information very quickly. 
2. TRADE ROUTE ESTABLISHMENT: Need some sort of trade route planner (maybe built through the economic screen) so you can see and understand how trade income potential varies depending on the location BEFORE you build the HQ + Subsidiaries.   Mechanics are the income numbers for trade routes are completely opaque right now.
3. POPULATION SCAN: This screen is horribly confusing.  I'd suggest removing it and instead make a new screen sort of like that economic scan.  It would show an alternate view of the starmap that visually summarizes the mix of species and party affiliations right on the systems.  It would make it easier to tell "where" you might need to do something about your population/party mix.  Hovering over a system could show a pop-up for the history of actions affecting the party on that planet.

Hi there!

Great post with a lot of well thought out points. You mentioned taking input, so I figured this seemed like a good place to post this.

To tack on to your comments about the Scan screens, I'm currently at a loss to to the meaning of one particular aspect of the Diplomacy screen: the count of connecting lines between systems. The "Links between other empires and yours," lines are straight forward, of course, but the "System link for each empire" is currently eluding me. It doesn't appear to be based on faction count within a given system, which is what I thought it was at first based on the description, and I have yet to find any other specific commonality between systems with the same count of links.

I've looked at the manual, which doesn't really detail what each scan screen does, and I've browsed the forum here quite a bit as well as perusing the ES subreddit.. am I missing something obvious on this one, or is the count of visible links purely aesthetic? Thanks!

Heh - I have no clue.  All of the "scan" screens look really cool but as far as providing usable information I'm not sure - yet.

I've been longing for a 4X game to make use of geographic data visualizations methods (hey, I work with GIS every day professionally!) - and I feel like these "scan" screens are heading in that direction, but they need to be made much more functional.  

Ideally, I'd like all of the scan's to be toggle-able overlay/filters that you can mix and match.  Would be cool to simply have a row of buttons (maybe in the bottom right corner below the end turn button?) for all of the scan modes so you can quickly turn any of them on or off.  It would make them much more accessible and useful - assuming the information they are intending to convey is clarified.