Having played around with beta 2 for some days here is my 2 cents:
1) The game seems very stable already. I have had no issues so far.
2) I really like the seamless zoom from overall galaxy down to detailed view.
3) Some more "life" in space would be nice. Like civilian ships, factories and similar to get a feel of a living universe.
4) The ability to build different types of ships seems a bit unbalanced. Frigates are available from the start as well as capital ships bit cruisers needs a lot of research. It would seem resonable that the capital ships needs the most research before they are available since they are the most powerful type of ship.
5) The tech tree feels a bit simplified and "disconnected". Maybe it could be expanded and divided into different areas such as : beam wepons, missile weapons, ballistic weapons, trade, diplomacy, ship hulls, manufacturing, civic development, terraforming, computers etc. Now you have for example one research button for a single type of ship and when it is researched you can build the ship. With a more granular tech tree you would need a certain collection of researched areas or components in order to build something, some components common between ships or structures and some unique.
This would also make it possible to build certain structures or ships early but in a less powerful version. If you have researched for example very large hulls, capital ship engines and medium shields you could build a capital ship. However it would be very weak until you researched appropriate weapons, improved shields and performed an upgrade.
6) When zoomed in during battles the feeling that you are dealing with huge starships is missing, it feels more like chess pieces. I am not sure what is missing but more detailed graphics (moving turrets and pieces of debris falling of during damage for example) may be one way of improving this. I also think the movement of the different sizes of ships could be improved. Small ships like fighters moves in a very artifical way when they strike, stop, turn 180 degrees, strike and so on.
Overall i am really looking forward to this game being finished, keep up the good work !