Not sure if what I've written below is fixed in 1.02, as I haven't had the opportunity to download it and play it yet. If it is, please let me know.
Also I included the link to the reddit post I made about this issue, some other players also had similar problems it seems.
Playing anywhere beyond 3-4 hours (it seems) causes the game to stutter and slow down, to the point where it is unplayable. Upon reaching the point where it is unplayable, and slowly but surely managing to exit the game, I found the GalCiv3.exe running in the Windows Task Manager for a good 3-5min after I had fully exited the game (it wasn't showing up on the desktop taskbar). It was chewing up a good 2GB+ of physical RAM, and was slowing my whole PC down (seriously, couldn't open any other applications, and I lagged my way into opening the Windows Task Manager). This seems like a pretty obvious memory leak in the game, no?
Additionally, having just passed turn 310 in my Terran Alliance campaign (playing on an Immense-Size, tight-cluster galaxy map with all available default races on the 'Challenging' difficulty), the game simply crashes every time I try to save, and doesn't actually save the game (even auto-save doesn't work).
The game at turn 310+ is also much slower and seemingly buggier (sounds not playing, random slow-downs, etc.), it's still playable, and I can still go to the next turn and do things (although quite slowly)... but like I said it crashes when I try to save. 
Anyone here know if Stardock is aware of this? Can we expect a fix in 1.1 (or is this fixed in 1.02)?
Thanks,
~Caesar.
P.S: I know that they fixed these issues in patch 1.02 (quoted from the 'Performance' sub-section of the patch notes):
"Fixed leaking refs in gizmo gfx
Fixed leaking refs for selected component in ship designer
Fixed leaking refs for focus node in battle viewer camera updater node"
But I'm not sure what any of that means...