Would love to contribute actively to this game and think this was missing until now.

Although it is still early in game development and many items might be up for change,

it probably won't hurt anyone to start collecting suggestions and it might even help the devs, right?

This is what game menus I could think of right now:

Start screen
Clear enough. Nice that space brings up extra information here as well. Am I right in assuming it is only the one about the Cravers?

Galaxy view
Seems really well thought out. Good to see from a distance what every planet is producing, how many pops there are, what resources are there.
Suggestion: maybe add a little bar next to/underneath the system name showing the happiness of the people in this system? Adding this would almost make the Systems Management list obsolete for me.
Suggestion: and also, please add the same bar to the top left box. Just copy and paste the Empire Approval bar from the Empire Summary screen please.

Suggestion: There is something going on with the visuals of the rings around a system (as discussed here), mouseover should bring up exactly what that is, I think. It involves sieges, manpower, economy,...?

(Personally I think the fog of war-visuals somehow represent some hilly or mountainous landscape rather than undiscoverd space, but that might be more visuals-related then UI. As suggested here as well btw)

Notifications
Work well. Suggestion: add a little icon to directly launch (create new fleet) a newly build ship directly from the construction notification. It is a waste of time to open the Star System management screen for this every time that happens -which is a lot.

Enhanced - Diplomacy

This does not make any sense. When another home world is found, the relation is displayed. Clear enough. What do the direct links and the system links (especially messy) add?
Suggestion: clearify or remove entirely. Maybe replace with Systems Management list.

Enhanced- Trade
clear enough

Enhanced - Economy
not really sure what this adds besides a sumup of the previous screens. The blurry squares (why are there more than 6 colours used?) do not provide much intel.

Enhanced - System
(disabled for now)

Star system management

Suggestion: Not really sure about the placement of mouseover information. At this moment it is either presented in the small left bar of the screen (which is confusing if you're hovering over an icon all the way to the right of the screen),

or next to this small bar (if you're hovering over anything in the bar). Why not attach the information box to your mouse pointer to avoid all this?
Suggestion: All planets display how much base values they could produce. Grey this out if it is not used. 

Suggestion: It is not really clear how Planet Productions add up to System Production. The base values in system production don't seem to match with the displayed raw planet productions added together.
This could be clearified by showing the number actively contributing to system production next to the base values, for example.

Suggestion: please make an option to set automatic fleet creation and rally point on systems. Selecting every ship manually and sending it to a system to create a large fleet will get rather tedious in time.

Enhanced - Populations/Population Screen
these are being discussed here
suggestions from numerous people: more tooltips! and also, clearify the meaning of the top circles, The second rings should not be a gradient and should be solids with remaining slots always last,
replace the bottom arrow with a single pie chart and add an overview of all races you encounter. So you can see how they will be effected before you assimilate them.
Suggestion: maybe combine the double spheres for each planet?

Empire Summary
fine

Senate Screen
As allready suggested by XDAvenger93: for example in the economy screen you acces tabs from the top of the screen, in senate you acces the population tab from a buton on the bottom of the interface that does not even look like a button

Economy Screen

Suggestion: this should just be the Trade and Resources screen. For unclear reasons, this is the only combined screen under a single icon. Please give the Systems Management Screen a seperate icon. Or place it under Enhanced Galaxy view (see suggestion above).

Technology Screen
UI is already being reworked, see here.

Militairy Status
fine

Hero Management and Hero Overview
suggestion: Hero Overview is the only screen in the game (I can think of) you need to close in the bottom left. Please move this to the top center as this is confusing.

Quests and Events
fine

Diplomacy Screen
is unclear I think. Player relations are sorted from left to right by hostility if I'm right. That's confusing as they tend to hop places now. Please keep them in the same place.
I like how the colour of the field between them and me shows their opinion and the symbol the official relation. In this way, the screen tells almost everything in a glance.
Except for the fact that the faction portraits are sometimes covering part of the relationshipsymbol and there is a seperate button to place another faction in the middle and see their relations.
Why not place the player in the outer ring of the circle as well and display all known relations directly in the diplomacy screen (coloured link with a symbol, as it is now).
With multiple players that might look confusing at first look but this could be solved by highlighting the players relations by default and highlighting another factions relations as you mouseover their portrait.

That's all I could think of for now. Please let me know if you agree on what I'm stating here (sorry, it has become quite the list allready) or if there's anything more to add!

-Note to self: check this list with this post, remove obsolete suggestions and try and combine the two.-

I don't know if this has been mentioned yet, but in the Election screen, when the system is tallying up representatives of each party from your empire's various systems and planets, the information you are given to that respect (ie. how strong the presence of whatever particular party is) is perhaps a bit too simple. Currently, the number of representatives on each planet is represented by dashed lines, and you are given a sort of cumulative tally via coloured bars corresponding to the various parties. 

I found myself wondering how many representatives on my planets belonged to the individual parties being represented in that system; I could only make a vague guess as to the actual strength of a party by paying attention to the change in the coloured bars when cycling through systems. I'm not sure how important this kind of information actually is, but I thought it would be nice if the UI could show what party each representative in a system belongs to, by colouring each line the colour of the corresponding party. That way it would be pretty clear where that system is on the political spectrum.

Thanks for the suggestions, it helps.

For your information, the tabs in the Economy Screen have been changed in the next update to fit to the rest of the game better. They make sense because they change the content of the screen. We'll have more tabs like that because we lack space for buttons in the control banner.

As for the "button that doesn't look like a button" in the Senate Screen, it's not a tab because it opens a modal window (like the assignment buttons in the Academy for instance). About the button look, it is just like the other buttons in the game, really... a circled icon, often with a text beside. The fact that you don't seen it as button worries me a bit :-S

The Diplomacy Screen has its problems, you're right, and we are thinking about potential improvements.