A word of warning, be aware that any ideas/suggestions/preferences I have are going to be biased by my love of gigantic galaxies and the fact that I haven't played with GC2 rally points yet. Several ideas I've not seen discussed here follow.
First idea, I'd like a way to go straight from the dropdown icon on the right to launching, without going through the starport screen first. I definitely think that right and left click should stay as it is, and that double-click would be too error prone, so I think that restricts the idea to middle click (which I'm fine with, I have a middle mouse button, or at least a roller that acts like one) or shift/ctrl click. Maybe both/all three or allow a user preference to switch between them. Maybe a click and drag action, though that doesn't seem intuitive at all.
Second idea, and CariElf is going to hate me for this, I think the auto-govenor -upgrade needs a rethink. Having everything autoupgrade when a new improvement is available is a good idea, but I think it might be better if the govenor made that decision, limiting it to one upgrade at a time, when the build queue was empty rather than when the tech is researched. One limitation of the current method was mentioned here already, that being that when you get a planet (by influence or conquest) current upgradable improvements aren't applied. This weekend, I found two more issues.
First, by scheduling the upgrades when the tech is researched, the queue can become rather full. If I go to a planet and tell it to build improvement X, then I think the default should be for that to be the current project, not something the govenor queued up, and as it stands now, I'd have to shift the new project up the queue.
Second, I played some research-intense games this weekend, and was researching follow-on techs faster than any of my planets could finish the upgrades, and I found that if one upgrade was already scheduled for a particular tile, the follow-on improvements wouldn't get scheduled for that tile.
Now, both of these, and the original issue, can be addressed by other means, and I'm not opposed to that. In fact, the current method gives the player a better feel for how many upgrades a planet needs, and mine doesn't, at least not without more work. However, i think my idea does have the benefit of consolidating all the autoupgrade logic in one place.
Third idea. Not an idea near so much as a missed GC1 feature. In GC1, there was a little window that listed all recent events near the lower right corner of the screen. in GC2, we have the summary and the dropdowns, but there's one important (at least to me, and I'd suspect to anyone playing huge gigantic maps) thing that we don't have any beginning of turn notification of. Lost battles. I had a gigantic map going yesterday where most of my core planets were defended by three large defensive ships, and everything else had one or two. Well, along comes a fleet, they fight, and I barely win, loosing two of the three ships. I didn't see anywhere where it told me which planet this happened at, and since there was still a ship defending it, there was no easy way to go around looking for an under-defended core planet. Having optional dropdowns for AI-initiated battles would be nice. Either drop them on the right, in a different color (red/yellow/orange/other non-blue, non-green color), or drop them on the left. Preferrably allow for different settings for how much babysitting I want to do (red-lost battle; orange, won the battle, but lost at least one ship; yellow, won the battle, but took at least 25% damage to one of the ships involved, maybe even green for battle won, just in case you wanted to check where it was, but only if they're on the left).
Final idea (for now). How about rather than just a "follow AI ships"/"don't follow AI ships", how about a third option, "follow AI (military) ships inside my area of influence"? I got nailed a couple of times because early on in a war, I'd garrison my frontier worlds, but would let the deep worlds build their own defenses. And along comes a transport ship, right past my frontier, undetected until it lands on a core world that I never saw because I turned off "follow AI ships". I can't turn that option on, not only does it take too long, but all the high-speed scrolling from ship to ship sets me up to get motion sick (not an issue of the game, just a personal weakness. I can play Doom, but I can't watch someone else play Doom for more than a few seconds without getting queasy, and watching the game yank the camera view from one ship to another has the same effect).
Ideally from my point of view, it could be broken down even more specifically, seperate settings for Allied ships, Neutral military ships, Neutral non-military ships, Enemy military ships, and Enemy non-military ships, but that would probably be too many options for normal people.