I just played a few turns with the new beta and wrote things down that came to my mind while playing:

1)

When i double click a tech in tech tree, the game should chose that tech and close research screen. currently double clicking does nothing over single click.

2)

When i double click on a planet it opens the planet screen. a single click does nothing. it seems that either a single click option is missing or you have to click too often.

3)

I would like an option to choose different galaxy map backgrounds (are there different ones?) the current one i play on is too busy imho.

4)

In the main screen, the empire management list (planets/ships/...) it would be nice to have different sorting options, for example sort planets by name, size, production, research and most importantly planet govern setting. sort ships by position (in enemy, friendly or neutral territory / out of date / type) and so on

5)

The mouse cursor should change on ai turn. i like to know when i am not in control. currently the only indicator is in the bottom right (end turn button)

6)

An option to set the tech tree as the default tech screen. i don't like the current tech screen and always go the tech tree. this options would safe a lot of clicks

7)

This is a bit of a larger request: An fleet management system, i.e. set up fleet templates (e.g. 5 fighters + 2 capital ships) and give shipyards the option to construct fleets (i.e. the shipyard will construct a fleet according to the template and send them to the way point where the ships wait and merge when the fleet is completed and only when it is completed you will get the idle ship notification) as well as to update fleets (for example if you get the capacity to add more ships to a fleet you update you fleet template and give shipyards the order to update your fleets, e.g. the produce the missing ships and send them to the existing fleets)

If you have your own suggestions feel free to add them