The most blatant technical issue i've run into is that the game does not handle being minimized very well. If i alt-tab out of it and come back, there's garbage all over the screen, and i have to scroll the map around and/or mouse over the buttons to get them to redraw. This in itself i could deal with, however if some other task steals control and forcibly minimizes the game (AIM does this frequently, and some other programs have done it on occasion) when i return to the game there's just a blank screen with a message that says something along the lines of "DirectX Surface Lost." Nothing i've figured out will get it back into a good state, i have to keep hitting the esc key and try to guess where the invisible "quit" button is to exit out and restart the game.
The AI does _everything_ for you, sometimes even when you tell it not to. I have autocolonization turned off, but after awhile new colonies started springing up on their own on new planets in systems i controlled, and ocacsionally in entirely new systems. (Often in systems i decided not to colonize for good reason, because all the planets sucked)
The AI does a crappy job on the military build queue, as noted in other posts, it builds _way_ too many troop ships and marines. It seems to do a better job on the infrastructure development, although I've not tried stealing away control from that aspect yet to see how i do.
Research and production are well steamlined, for the AI. You set percentages for different areas of research, and that's about it. Even examining the research tree to see how you're doing is difficult. Each research project has about five seperate stages from knowing nothing about it to being able to use it. Each of these stages is announced for each project in all areas of research. Once these projects are finished the AI immediatly starts building any new improvements on every area of every planet. You also get told when every one of these projects are completed. The result is that every turn you get a few dozen reports in your SitRep dealing with nothing but "Technology X is now viewable," "Research on Technology Y is complete," "Technology Z has entered prototyping," "Construction of Q has finished on Phazon III," etc, etc, etc, ad infinitum. After several turns of this you just don't care anymore. You look down through the list and think, "Hmmm, some planet i own just finished constructing an automated thingamajig, i didn't know i could build those. I don't even have any idea what it is or what it does. Oh well, the AI seemed to think it was a good idea."
It would have been far preferable if there were a lengthy build queue, and the ability to plan out and save generic queues in advance. Just about every 4x game has that feature now days, but if Moo3 does i haven't found it yet. This would have given you some sense of interaction. When a new building was researched, you'd look at it, decide which queues to stick it in, and actually feel like you had some involvement.
The ship construction tool allows you a lot more control, but is akward to use, and a lot less fun that ship construction was in MoO and MoO2.
The encyclopedia sucks if you're trying to look up specific information. A lot of planets have specials on them, however i have no idea what "Ancient Battle Damage" means and what effect it will have on a colony i build there. I've tried using the search function in the encylopedia, and found nothing. I've tried searching on everything i can think of relating to the topic, and nothing returns any results. Mousing over the special should give you at least a rudimentary description, and clicking on it should take you to the (non-existant as far as i can tell) encyclopedia entry.
When you encounter enemy ships or planets, your choices are usually "sit there," and "attack." There is no option to break off an run away before combat. If you do want to run, you have to choose to control combat, intercept the fleet (or choose to bombard the planet and hope they choose to defend) and then order the retreat once combat starts and hope the enemy isn't fast enough to do some damage to you before you warp out.
Diplomacy is nice, but not as good as Civ3. I've had fleets from neutral empires hover around some of my systems, which counts as a blockade, keeping supplies from other planets from reaching it. However there was no diplomacy option i could find to ask them to leave the system, and i didn't want to attack them without provocation and screw our relations. Once my planet had starved to death the other fleet choose to attack my remaining ships. Luckily i won, and was able to send another colony ship to restart the colony. Despite the fact that the other empire choose to attack my ships it did not start a state of war between us. A lot of that seems to happen, unlike in Civ3. I've had multiple combats with and spent several turns coexting peacefully with in the same system as empires the i officially had no diplomatic contact with, and no idea of how to initiate contact. When contact was initiated they didn't seem to care if i'd been blowing their ships up beforehand or not.
I've not had a great deal of experience with combat, but what little I've had has seemed akward, unclear, and not very fun, which is why i usually just cede control to the AI.
All in all, the AI does a pretty good job of playing the game by itself, and seems to resent you trying to take control of anything yourself. It seems like taking direct control would be fun, if you didn't have to fight the AI to do it, and there were tools to do so in the way you wanted (saved build queues and better ship design!)