2 very important things that should be fixed IMHO:
The Advent unit that pushes enemy ships away with its special ability is overpowered. Not so much because it pushes things away, but rather, because enemy ships that were pushed too far do not continue attacking. Rather, they will try to return to the spot they were pushed away from. If you have 5 units with the repulsion ability (I believe that's what it's called) you can just spam the ability while your enemy ships will spend their entire time trying to get back to the spot they were pushed away from. Doesn't work oh-so-well against the AI, but it basically makes other fleets useless in multiplayer as they essentially stop attacking unless their range is enormous.
Superweapons. I haven't used the Vasari one, and neither do I have much experience with the Advent one. However, I do know that the TEC novalith cannon is overpowered. I can just put my entire fleet + hangars on a planet close to the opponent, then put a novalith right behind that planet, and bomb the closest planet. 2 shots and they're gone. As long as you defend it, which isn't that hard, you're gonna win eventually through attrition. Heck, your opponent can have a bigger army, but if you defend your novalith cannon well, you will take out a couple of planets every 10 minutes. Forcing people to rush a planet because it has the capability of destroying your entire empire is retarded, since defending is it very easy. No weapon should be able to destroy an entire empire from lightyears away. At least give people a very expensive bombardment defense upgrade that greatly reduces damage. The novalith cannon should be backup for your capital ships as they're attacking a planet, but they should not be able to destroy an empire by themselves.
Something somewhat important:
A lot of the time a ship will attack, destroy a unit and try to leave to go back to the spot it started, just to stop 5-10s later and continue attacking. We also need to be able to attack-move fleets. So let us use the attack button to move fleets, which would make them move and then attack nearby enemies instead of just moving and ignoring them.
Also, you might want to look at Advent Defense Vessel vs TEC LRM Frigate. Defense vessels wreck LRM's to the point where it's not even funny. 24 supply vs 24 supply (6 LRM vs 8 Defense Vessels)=LRM dead with 6 Defense Vessels left. It's not that I like LRM's, but it's utterly retarded that Defense Vessels (which are supposed to be good against fighters/bombers) absolutely wreck LRM's.
You also need a select all of one type hotkey. I haven't found one, although I haven't looked all that hard. Just like ctrl+shift+click on an LRM to select all LRM ships on that planet. If there is something like that already, I apologize.
I could go on all day, and by the time I'm done testing a bunch of things I could write you a 10 page paper, but I doubt my suggestions will be implemented. Congrats on making a great game though.