[spoon]

Ok, here's that feedback...

The Map:
- The player in the Upper Left one less planet "available" than the other three players (there should be another planet in between the damaging warp to the lower left and that Methane planet).
- The map works well with two or four players, but not so good for 3 players (since the player sandwiched between the two players would have a harder time expanding). One fix would be to make the map a balanced 6-player map, since that would accomodate 2, 3, 4, and 6 players. Another approach would be to make the map out of "tiles" so you could line up your systems depending on how many players you have... maybe they could connect with themselves, or they could connect to a hexagonal hub...

Downtime:
You can reduce the downtime between players if you split up the turn so that each phase of the turn is done by all players before progressing to the next phase. For example, in a two player game, turn order would go like this:

Research - Player A
Reserach - Player B
Ship Purchases - Player A
Ship Purchases - Player B
...
Administration - Player A
Administartion - Player B

It's even better if you can do each portion simultaneously, by introducing things like simultaneous (hidden) orders or bidding. For example, in the research phase, you could flip over X research tiles (X being the number of players) then bid on each of the tiles (obviously you'd have to have more items to research than currently listed!) For the movement turn, each player could place hidden orders on each of his ships/fleets, and then resolve movement one order at a time, alternating between players. (check out the Game of Thrones boardgame for a good example of how this works).

Elimination:
I personally don't like boardgames of 3+ players where someone can be completely eliminated from the game (eg, Risk, Monopoly) since that means you could leave someone out of the "fun" for the rest of the evening! So I'd rather see different victory conditions, such as: "The first person to colonize X planets" or "The person with the most Victory Points after X number of turns" or a combination of the two. The latter two options also have the side benefit of being able to better control how long the game would take to play, making the game more appealing to people who have to "schedule" their time to play games...(ie, us married folk!)
But again, this is personal taste, so do as you will...

Research:
I thought that the research was too random, and didn't have enough choices. (I also couldn't find in the rules how Research Facilities were supposed to work, so that maybe that alleviated some of the randomness???). I would probably come up with significantly more options, and not let progress be determined by a die role. I like either auctioning research (as mentioned above) or simply buying research (with minerals or with "research points" that would be generated by research facilities (or a combination of the two)).

Movement:
I like simultaneous order giving. Two obvious Orders are Move and Defend - but maybe throw in some other orders for good measure (though they would obviously need mechanics to go with them) such as Retrofit, Patrol, Lay Mines, etc). Anyway, everyone places all their orders face-down, one order per ship/fleet. After all orders are placed, reveal them, and each player executes orders one at a time. (eg, Player A moves one fleet, then Player B moves one fleet, etc, etc.) In the Game of Thrones boardgame, certain order types are executed before others: so you might resolve all movement orders before you resolve Retrofit orders.

Combat:
I would simplify it where possible: I'd get rid of the "called shot" (though possibly make a researchable component that lets you do that). And I'd also get rid of the defense roll... the attack roll is probably good enough. (ECMs could work like so: Any ECM in the enemy fleet reduces/eliminates the Combat Sensor bonus of all ships in the other fleet).
I wonder if keeping track of damaged components is too hard or not, but I like your idea and would playtest it (I also wonder if moving the ships around the map would also cause problems (ie, it would be difficult to tell at a glance what forces an enemy has in any given system - you'd have to pick up each fleet and flip through the ships, while not messing up the components on the ships...)