I have run into the problem where the UI seems really sluggish for me.

My first issue with the UI: its very obtrusive sometimes. For example the robot movie that shows when you complete a research project. I would love to see an option that lets you disable that.
Maybe make it so that research projects only show you those small alert icons that drop down the right side of the screen, similar to whats done when a ship is built.
The same is true when a sruvey ships goes into standby mode after having explored all anomalies. I really don't need a popup to tell me that. Another alert icon on the right hand side of the screen would be enough.
This is a problem because later in the game, when all anomlies have been surveyed and you only get 1 new anomaly every so many turns it kinda gets annoying. I love playing small maps and my 20 speed Survey Ship will get there in one turn (most of the time). Meaning that I get that standby message way too often.

My second issue is that the UI is very sluggish and screens that are logically tied to each other don't really show instantly after another.
There are many examples for this, but consider the screens that show in the event a research project finishes. First the robot movie is shown, then the research screen is shown where you can select the next research project.
Normally you would expect those to show instantly after another. But they don't. For me it can take up to 5 or 10 seconds for the research screen to appear.
My computer can run GalCiv2 perfectly and the considerable delay between screens causes the following problem. I play fps games, I like to click fast. After I clicked that robot movie away I keep playing, I keep moving fleets, setting espionage levels, queue planetary improvements. Then suddenly after 5 or 6 actions that research screen suddenly pops up. Most of the time it closes the screen I was actually looking at.
I don't get why you get bumped back to the game window after the robot movie, instead of going straight to the research screen?

My third suggestion is about battles. As you know, there is an option that lets you set how detailed space battles should be shown. There are 4 settings: Full battles (cool space combat cinematic), Normal Battles (battles are fought on the galaxy map), Quick Battles seem to be the same as Normal Battles, and Instant Battles are as the name says instant.
My problem is that the "quick battles" aren't quick enough. While its great that the camera is moved to the battle on the galaxy map. Resolving the battle takes 5 seconds or so. This is because first weapon fire is shown, then the resulting explosion. If - for example - you do have a ship with ton of different weaponry, the firing bit of the battle can take quite long (use fights against fully upgraded Starbases as a perfect example). How about making "quick battles" really quick? Remove the weapon fire part or cap it to only last a maximum of 0.25 seconds, and make the explosion also shorter, to maybe only last 0.5 seconds. I really only want to be able to see the result when I elect for quick battles. I don't want eye candy or see a space battle being fought.

To sum up my experience with GalCiv2: It promotes something I would like to call "grandpa" playstyle. If I take a break of several seconds between each action, if my eyes have weakened to the point where I need visual cues to be present for seconds instead of fractions of seconds for me to notice ... then the game is fine. But if you want to play fast, the UI sucks.