Hope none of this is redundant. Also, don't misunderstand these thoughts and think I don't like the game. A continuous string of suggestions and constructive criticism starts to sound like badmouthing after a while ...
Logistics should be partially based on the size of your civilization. A tiny civ that happens to have awesome research capabilities may be able to field as many capital ships as a large civilization with poor logistics technology, but a huge civ with decent technology in war-production mode should still be able to field more ships than the tiny civ can possibly manage. So perhaps logistic points should be calculated not only from technology but also from military spending, overall resources, population, etc. Of course, maintaining such huge fleets would be terribly expensive ... Also, really large civs wouldn't be able to quickly transfer resources, troops, and ships from one side of their territory to the other; civilian cargo ships have limited engine capacity, too. Perhaps logistics points from each world and station should be split between the fleets nearest them; a certain number of ships can be supported in each region without undue economic hardship -- but the more ships concentrated in one place, the more difficult it becomes to maintain them. A system like that should also include the option of whether or not to have regions help support far-away ships, and supporting ships should be detrimental to local interests as materials flow out without so many flowing back in exchange. Support from far away could be made less effective than nearby help, much as asteroid belts function. In fact, the entire logistics system could be treated very similarly to how industry points from asteroid mining bases are treated, with players being able to select planets and stations and assign them to "send" their logistics points to specific fleets or ships, even splitting points from a single planet between several fleets. Perhaps you could also make it so that ships do not actually need logistics points to function, but lacking them means that the commander simply requisitions all necessary materials from nearby systems -- resulting in penalties to production, morale, ship efficiency, and (if you're neutral or evil and/or the citizens are displeased enough to riot) population. Finally, ships in enemy or non-allied territory will either need to carry all provisions with them, pirate, set up resource gathering points/dumps, or depend on supply lines. The first requires economic buildup beforehand and might be spotted via espionage; the player should choose whether to have a long, slow, difficult-to-detect buildup or a rapid and obvious one. The second one is somewhat dangerous, would boost or degrade your morale depending on factors such as your alignment, and doesn't always work. The third requires intensive defense if you want the resource gathering points to survive for any length of time, although sometimes you might not. The fourth might be very like trade routes and would make you vulnerable to flanking maneuvers, although you can always resort to piracy if your lines are successfully cut by the foe. When passing through allied space, ships could either use one of the above four options or rely on the ally for resources; in fact, whole new treaties could be based around buying the right to have someone else logistically support your fleets for a while (caveat emptor if the other party is an enemy).
On a related note, GalCivII portrays you, the player, as a normal person. If this is so, where are the communication breakdowns and fleets whose location is unknown because they haven't reported in? The ambushes by sensor-stealthed enemy forces that wipe out a fleet before it can call for help, the decoy ships that have you scrambling defenses before you realize they're made of cardboard? The misunderstood instructions and the orders lost due to enemy jamming or solar flares? Effective communications relays, communication technology upgrades, sensor networks, and the like are needed if the player's avatar in-game is truly mortal. The only logical non-metagame reason for the flawless communications and scanning abilities in GalCivII are a) continuous, incredible luck,
the fact that the player is actually an energy being capable of flawless telepathy reaching all corners of the galaxy instantly and perfectly, or c) the institution of an incredibly complex multiple-redundancy/high-tech network requiring money and time to implement. Lots and lots of money. And you thought being the monarch of an intergalactic empire meant you never had to pay a phone bill again
Seriously, in most wars communications are impeded frequently. The increased effectiveness of future communication systems should be balanced by the vastly increased ranges across which transmissions must pass, better jamming technology, and bigger natural events that could interfere. (Supernovae or gamma ray bursts, for example) A fleet out of communication could be controlled by the AI -- if you don't like what the AI does with your fleet, well, admirals don't always like what their captains do when cut loose from direct supervision and deprived of effective intelligence about the enemy. It would be necessary to put in some provision for either giving preset orders or maintaining communications if the signal loss is deliberate, though. Many times a military unit has chosen to cut transmissions to their base so the enemy can't detect them, or has used electric landlines or written message drops for similar reasons. Ideally, you could send a group to hide in a sensor-distorting, communications-killing nebula; give them orders to come out in three weeks, set up a stealthy courier ship, or even resort to running a fiber-optic cable from outside the nebula in to the hidden ships to stay in touch.
On the subject of treaties, it seems slightly illogical that GalCiv civilizations can research technologies like Majesty, surrender to each other, establish treaties like Eco/Tech/Normal Alliances, and turn themselves into Star Federations without being able to ALSO incorporate alien cultures into their own. Or vice versa. Admittedly, wariness of other cultures and species is a powerful force -- but if you're Altarians and have had a firm alliance and cultural edge on the humans for fifty years with intensive trading and interaction between you, a complete merger of government is not inconceivable. And minor races might quell their own pride, independence, and fear in order to gain permanent protection by a powerful patron. They might even bring a few advantages with them. A game that exemplified this possibility was Birth of the Federation by Microprose. Something would have to be done to balance this, though, or else the Yor and Korath would suffer because no one would join with them. At least, no one with a brain. Alternatively, you could simply point out that isolationist nations often perish and leave it that way, making playing either of those races an added challenge. You could also add the option of enslaving the entire other race if you take their planet/s, although this tastes more like something the Drengin would do.
How about taking advantage of all that unused space in the colony capital? Add modules/upgrades for the capital so you can customize it for whatever you need it to do, or at least make it more than just decoration on the landscape that takes up a square.
Lastly, where are the rare but possible defections or mutinies that steal an entire ship from you? And where are the astronomical objects/events like black holes, neutron stars, nebula, etc?
The only game I've ever found comparable to GalCivII in terms of quality is Birth of the Federation. I very much prefer GalCivII, and BotF had many flaws of it's own, but there are quite a few things from BotF that would be worth looking into as ways to enrich GalCiv. EDIT: Looking back on some of the other posts, I see that upgraded planet/system defenses have been suggested. This is a great example of how many strategy games could benefit from looking at BotF, which had a good system that combined shield generators and anti-ship weapons with orbital batteries.
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the fact that the player is actually an energy being capable of flawless telepathy reaching all corners of the galaxy instantly and perfectly, or c) the institution of an incredibly complex multiple-redundancy/high-tech network requiring money and time to implement. Lots and lots of money. And you thought being the monarch of an intergalactic empire meant you never had to pay a phone bill again 
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