Ok a few more things I thought of:
6) There are times when I just want to stay in my own little corner of the galaxy to built up my armada. Sadly the stupid little asteroid mining ship goes all the way out to the edge of its range mining asteroids that I can't even see! I'd love a way to limit automated vessels to a certian "range". For example, if the mining vessel would only mine those asteroids that you can actually see even if there is another group 1 square away from where you've explored. Maybe something along the lines of "restrict vessel to X# of sectors/parsecs from world of origin."
7) This is something that has always irritated me. What's the use of having level 4 sensors when every race you meet reguardless of their level of sensor technology sees you as soon as you see them? If you're going to seperate the effective range/Linoe of Sight for different sensor levels, have it mean something!
8) Occasionally I'll use colony ships as scouts, I'll click somewhere is the vastness of unexplored space and send them off (especially once I've built the Eye of the Universe!). Every so often that random click is a really crappy planet (PQ1 or 2). I'd love it if there was a way to double check with the player before actually colonizing the planet. (I'm thinking a flag to mark that the destination was covered in the fog of war and when the ship gets there if said flag is true then prompt the player maybe?)
9) As many others have stated, the ability to add copious amounts of flavor text and/or background history for any user created races and have said history used by various prompts in-game. (Alpha Centari was very good at that!)
10) I'm not sure if this is a setting I've neglected or if it's due to somethign else but every time I run across an Major race, if I have built starships with weapons/armor then all is well. If I haven't then usually within 5 or 10 turns the AI starts threatening me. How does it know what ships I have? Is there an added level to espionage that I don't know about?
11) I seem to recall reading somewhere that the AI knows where the resources are because "they had explored that region of space prior to the invention of the hyperdive" or something like that. That's fine when you're playing the Terrans but how come you don't know where those same resources are when you're not (playing the Terrans)?
12) Where are those stargates anyway? The ability to use those as an alternative method of travel would be interesting (as someone else has suggested). I would, however, place some linitations on it such as:
I) Limit the number of vessels per turn that can use the gate. A branch of the tech tree could research ways to increase this number. For an added twist only half of that number can be going in either direction. ie, a level 5 gate could have only 5 ships going from A to B and only 5 ships going from B to A. If the civ at endpoint A has researched gate tech then the gate might allow them to send 6 or 7 or 8 (depending on thier level of gate tech) in either direction while civ B (without any gate tech) is limited to the default gate rating.
II) The advent of hyperdrives means that the stargate system has fallen out of favor and no one is really sure how to make it work anymore. After extensive research, the knowledge to use the system is reclaimed. However, the gates must be linked together at each end meaning you still have to travel there the old fashioned way atleast once!
13) I like the idea of pirates, possibly as a "spoiler" race. A minor (possibly major?) race that players can negotiate with, pay tribute to and bribe to create havoc with other races major and minor. A (small? increasingly greater?) chance for them to turn on the player and "bite the hand that feeds them" shouldn't be overlooked either!
14) Some of the random events are too game altering especially if you get tag-teamed by them. I once had a random event (my diplomat upset them at a state dinner or something) and suddenly I was at war with the race that had, the turn before, been paying a tribute to my greatness. Since they had been sucking up to me I didn't have many ships there and viola, a few turns later no one travels faster than a speed of 5 for the rest of the game. On an immense map, that's torturous! I would like a way to prevent combinations like that from happening (or to ensure they happen on higher levels of difficulty maybe?)
15) Speaking of random events, I'd like a way to edit them. Even if it's only to weed out the ones I really don't want to happen. The ability to add or alter existing events would be icing on the cake 
16) Another one of my pet peeves, I'd like a way to increase the IQ of the AI without affecting their economy. Ideally I'd like a smart AI that has the same, if not few resources than I do. Sometimes I want to win while only working up a little sweat. (Hey, I'm playing this to have fun, not audition for the role of Galactic Saviour (What? No one besides me remembers "The Last Starfighter"?))
Ok, that about does it for now. Thanks for listening to my rant!