It's pretty obvious that a lot of the players have no fully played the game before writing what they think. I have played about 1000 turns worth and although I certainly do not know everything about this very complex game, I know a fair bit. I'll break it down into several core game issues.
Diplomacy: This is quite possibly the worst diplomacy I have seen. Each race has pre-determined attitudes against you, for example if your races had a war back eons ago they will hate you. There is virtually nothing you can do to fix this, you can trade with them for 300 turns and they will still hate you, it's ridiculous how diplomacy is more based on past events out of the scope of the game than what the player actually does. There are very limited actions you can take, for example you can only ask allies to attack one race at any given time. If you are in a war with someone and you want them to join? Tough luck. You want to join the Orion Senate? Can't do that either, hope that the AI decides to vote you in (never). I could go on, but you get the idea.
Espionage: Another terrible implementation. The way it works is that you can train a spy in x turns that do one certain task. Now, this wouldn't be too bad, except you can only train one spy at any given time, and they die by themselves over time. What this means is that you cannot reasonably use espionage because you'll be screwed out of defense if you commit a spy to attack (unassigned spies work as defensive units). The upkeep is this ridiculously low amount that would barely dent the economy of one planet but somehow your huge 100 planet empire is restricted to 10 spies because they die by themselves. The game also has this novel idea of leaders that give your entire empire a bonus, however, the game is set so they die ultra easy to espionage. If someone is after your leaders you might as well kill them yourself, they die in 10-20 turns guaranteed, no matter how many political counter-spies you make. This is just one of many nonsensical ways that espionage is used.
Battles: The game forces you to play at 800x600 resolution, which basically means that you can barely see anything in the battles, and if you zoom out everything is ultra tiny. The fleet you spent hours building is all but 5 grey specs on the screen, you have no idea what they are doing or how far you are away from the enemy. More ugly pixels just spew out and you hope that it does some damage. From what I can tell, certain things don't work all the time, so your carefully crafted counter to enemy ships will just not work and you will get beat down. Tough luck, reload and you will win with 0 losses. Then you have ground battles where you have a huge menu of 2 dozen or so options to attack/defend a planet, and from what I can tell it basically tells the game to play different sound effects for you. The effect of these options is completely undocumented and all of them seem to do the same thing. Transports automatically disband after attacking a planet and you need to wait 5+ turns before getting to use them again.
Planet Building: A definite improvement over MOO2 in terms of reduced micromanagement, and the AI is actually fairly good at figuring out what to do. However, there is definitely too much that ONLY the computer can do. As a human player, you cannot build any additions to core buildings (ie, 99% of planet building), all you can do is configure rules and hope the AI builds what you want. Even so, I think planet building is a huge improvement, and completely necessary considering how bad the user interface is. It would take you years to manage your planets every turn if you had to do it manually.
Since this is getting pretty long, I'll just wrap up with a summary. Overall, MOO3 is a very boring game even from the eyes of a fan of strategy games. Unless you consider playing with spreadsheets fun, this is probably not for you. The graphics, sounds, user interface, help system, etc, are all sub-par and will test your patience for sure. Terrible implementation of several core systems as mentioned above and many annoying glitches/game design decisions will keep you from enjoying the game.